using the hp-12c calculator: the b asics welcome to {organization}

Using the HP-12C Calculator: The Basics

Welcome to{Organization}

Instructor [email protected]

Your Instructor Today is

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Instruction Method

• Lecture

• Illustrations

• Practice Problems

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Text for this course…

Using the HP-12C Calculator: The Basics

Publisher:Hondros Learning™, ©2009

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Course Objectives

Upon completion of this course, you will be able to:

– Compute basic functions of the HP-12C financial calculator.

– Describe the process of Reverse Polish Notation.

– Compute complex calculations combining arithmetic functions.

– Practice various mathematical problems using chain calculations.

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Course Objectives


– Explain the basic functionality of stack registers.

– Describe the purpose of prefix keys. – Practice using a prefix key to change decimal

settings.– Practice using the storage and recall functions

of the HP-12C.

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Course Objectives


– Exhibit how to clear one or all registers.– Solve typical appraisal percentage problems.– Describe the concept of the Time Value of

Money.– Describe the six functions of a dollar.

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Course Objectives


– Identify the financial register keys and explain the function of each.

– Practice computations using the financial registers.

– Explain cash inflows and cash outflows.– Practice calculating net present value and

internal rate of return.

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Course Objectives


– Determine whether or not to accept or reject a project or investment.

– Practice using the HP-12C to calculate the mean and the standard deviation.

– Demonstrate how to calculate both the mean and the standard deviation in the same problem.

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Course Outline

Chapter 1: Simple and Combined Arithmetic Functions

Chapter 2: Chain Calculations and Prefix Keys

Chapter 3: Data Storage Registers and Percentage Problems

Chapter 4: Time Value of Money Functions

Chapter 5: Net Present Value and Internal Rate of Return

Chapter 6: Statistical Calculations

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Chapter 1

Simple and Combined Arithmetic Functions

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Objectives

1. Compute basic functions of the HP-12C financial calculator.

2. Describe the process of Reverse Polish Notation.

3. Compute complex calculations combining arithmetic functions.

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Terms to Remember

• Reverse Polish Notation (RPN)

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• A financial calculator is a necessary tool for today’s real estate appraiser.

• Appraisers can perform complicated and time-intensive financial calculations quickly and with much greater ease.

• Most appraisers acknowledge the Hewlett Packard HP-12C calculator as the standard of the appraisal industry.

Why Use the HP-12C Calculator?

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Why Use the HP-12C Calculator?

• Some states require coursework specifically addressing problem solving with the HP-12C.

• Many advanced appraisal courses focus specifically on applications using the HP-12C.

• The 2008 National Uniform Appraiser Examination will present mathematic problems that must be solved using a financial calculator; proficiency in the use of a financial calculator is no longer an option!

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The Basic HP-12C Keyboard

• The keyboard of the HP-12C calculator is designed in a horizontal pattern as opposed to the vertical pattern found on most calculators.

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The ON Key

• The [ON] key is located in the lower left hand corner of the calculator keyboard. The HP-12C has no “off” key.

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The Arithmetic Operation Keys

• The arithmetic operation keys (+, -, x, and ÷) are located vertically to the far right of the keyboard. The HP-12C has no equal [=] key.

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Number and Decimal Keys

• The number keys and the decimal key are located immediately to the left of the arithmetic operation keys.

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The ENTER Key

• The [ENTER] key is a vertically-elongated key and is located at the lower part of the keyboard, just right of the keyboard’s mid-point.

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The CLEAR Key

• The [CLX] key clears the number in the display and, in simple arithmetic calculations, the entries for that calculation.

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On, Off, and Clear Functions

• The HP-12C calculator is always turned on manually and can be turned off manually by using the [ON] key.

• It will turn off automatically after 8-15 minutes of being idle.

• Any numbers in the display are NOT erased when the calculator is in the off mode.

• Often, errors occur from not clearing the calculator when turning it on to begin a new calculation.

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1. Turn the calculator on by pressing the [ON] key.2. Make certain the calculator is cleared by

pressing the [CLX] key (display should appear with all zeros).

3. Using the number keys, press [2] and then [5] (25.00 should appear in the display).

4. Turn the calculator off by pressing the [ON] key.

(continues on next slide)

Try this…

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5. Turn the calculator back on again by pressing the [ON] key (25.00 should appear in the display).

6. Press [CLX] to clear the display (display should now appear with all zeros).

Try this…

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Simple Arithmetic Functions

• In simple arithmetic calculations, two numbers are always involved and are either added, subtracted, divided, or multiplied.

• Standard calculators and some other financial calculators use algebraic input for simple arithmetic problems.

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Reverse Polish Notation (RPN)

• The HP-12C employs a method of inputting numbers for simple arithmetic problems known as Reverse Polish Notation.

• Reverse Polish Notation (RPN) is a formal logic system used in the HP-12C calculator that allows mathematical equations to be expressed by pressing the arithmetic operation key (+, -, x, ÷) after the numbers or variables have been keyed.

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Simple Arithmetic Functions Example

• With a standard algebraic calculator, the keystrokes for 5 plus 5 are [5] [+] [5] [=].

• To find the sum of 5 + 5 on the HP-12C, the keystrokes are [5] [ENTER] [5] [+].

• The solution to the calculation will be displayed immediately after pressing the [+] key.

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To add 5 plus 5, the keystrokes are:

[CLX] (clears the display)[5][ENTER] (separates the input and tells the

calculator that you have finished the first entry in the calculation)[5][+]

Result: 10.00 should be displayed.

Try this…

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Try this…

To subtract 6 from 10, the keystrokes are:

[CLX][10][ENTER][6][–]


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Try this…

To divide 60 by 20, the keystrokes are:

[CLX] [60][ENTER][20][÷]


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Try this…

To solve the multiplication problem of 5 times 20, the keystrokes are:

[CLX][5][ENTER][20][x]


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Combining Arithmetic Functions

• Frequently, appraisers must employ calculations that combine a series of input that use addition, subtraction, division, and/or multiplication.

• While many standard calculators also allow this in similar function, the keystrokes will be different.

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Lot Size Stated in Acres

• To find the area of a building lot or parcel the formula is:

Frontage x Depth = Total Square Feet ÷ 43,560 (square feet in an acre)

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Lot Size Stated in Acres Example

• The appraiser is trying to find the lot area, in acres, of a building lot that has 135 feet frontage and 220 feet depth.

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Try this…

[CLX][135] [ENTER][220] [x][43560] [÷]

Result: 0.68 should be displayed. This is the lot area in acres.

Important: Do NOT press [CLX] as we will use this result in the next calculation.

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Usable Site Area by Percentage

• When the appraiser determines the percent of a parcel that is usable, one additional calculation can determine the usable area.

• Assume the appraiser has estimated that 75% of the parcel is usable.

• To complete this calculation, the percent key [%] is used.

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The Percent Key

• The percent key is located in the second row from the top, fifth key from the left.

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Try this…

The answer to the previous example should still be displayed (0.68).

[75] [%]

Result: 0.51 should be displayed. This is the usable area in acres.

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Square Yards

• There are nine square feet in each square yard.

• The calculation to determine square yards is:

Length x Width ÷ 9 = Square Yards

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Square Yards Example

• An appraiser is determining the number of square yards of carpet for a room that is 12’ x 14’.

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Try this…

[CLX][12] [ENTER][14] [x][9][÷]

Result: 18.67 should be displayed. This is how many square yards of carpet would be needed.

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Cubic Feet

• A cubic foot is a unit of volume.

• Cubic feet are calculated as:

Length x Width x Height (or, in some cases, depth) = Cubic Feet

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Cubic Feet Example

• An appraiser is determining the cubic feet contained in a building that has ground dimensions of 100’ x 75’ and is 18’ high.

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[CLX]

[100] [ENTER]

[75] [x]

[18] [x]

Result: 135,000.00 should be displayed. This is the number of cubic feet contained in the building.

Try this…

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Cubic Yards

• There are 27 cubic feet in each cubic yard. Cubic yards are calculated as:

Length x Width x Depth÷ 27 = Cubic Yards

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Cubic Yards Example

• An appraiser is determining the cubic yards of concrete needed to install a patio that will be 15’ x 18’ and 6” (0.50 foot) thick.

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Try this…

[CLX]

[15] [ENTER]

[18] [x]

[0.50] [x]

[27] [÷]

Result: 5.00 should be displayed. This is the number of cubic yards of concrete needed.

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What you have learned…

• How the calculator is turned on and off.• Number(s) keyed into the calculator (or a

part of a calculation or the solution result) remain in the display and memory.

• How to clear previous calculations using the [CLX] key.

• Simple and combined arithmetic calculations using RPN.

• How to use the [%] key.

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Chapter 1 Quiz

1. A one and one-half story residential dwelling has 1,400 square feet of gross living area (GLA) on the first floor and 546 square feet of GLA on the second floor. What is the total GLA of the dwelling?

Correct Answer: 1946

Keystrokes: [CLX] [1400] [ENTER] [546] [+]

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Chapter 1 Quiz

2. How many acres are contained in a parcel that has dimensions of 366’ x 407’?

Correct Answer: 3.42

Keystrokes: [CLX] [366] [ENTER] [407] [x] [43560] [÷]

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Chapter 1 Quiz

3. A jurisdiction allows for 65% of a residential building lot to be covered by the primary dwelling. What is the square footage of the first floor of the dwelling if the lot dimensions are 110’ x 165’? Round your answer to the nearest whole number.

Correct Answer: 11,798

Keystrokes: [CLX] [110] [ENTER] [165] [x] [65] [%]

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Chapter 1 Quiz

4. Determine the total cost of carpeting a room that is 22’ x 18.5’. If the carpet costs $38 per square yard installed, what is the total cost of the carpet?

Correct Answer: 1,718.44

Keystrokes: [CLX] [22] [ENTER] [18.5] [x] [9] [÷] [38] [x]

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Chapter 1 Quiz

5. A storage building is 25’ x 30’ and is 12’ high. How many cubic feet are contained in the building?


Keystrokes: [CLX] [25] [ENTER] [30] [x] [12] [x]

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Chapter 1 Quiz

6. A residential dwelling has a total gross area of 1,830 square feet. Included in the gross area is a porch that has 260 square feet of area that will not be included in the total gross living area. Excluding the porch, what is the total gross living area of the dwelling?


Keystrokes: [CLX] [1830] [ENTER] [260] [-]

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Chapter 1 Quiz

7. If a parcel of land contains 38,000 square feet and can be divided into three building lots of equal size, how many square feet will each building lot contain?


Keystrokes: [CLX] [38000] [ENTER] [3] [÷]

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Chapter 1 Quiz

8. The fenced-in portion of a rear yard is 52’ x 37’. How many square feet does the fenced-in yard contain?


Keystrokes: [CLX] [52] [ENTER] [37] [x]

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Chapter 1 Quiz

9. Determine the total cost of carpeting a room that is 16’ x 20’. If the carpet costs $32 per square yard installed, what is the total cost of the carpet?


Keystrokes: [CLX] [16] [ENTER] [20] [x] [9] [÷] [32] [x]

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Chapter 1 Quiz

10. An office space is 30’ x 65’ and is 10’ high. How many cubic feet are contained in the building?


Keystrokes: [CLX] [30] [ENTER] [65] [x] [10] [x]

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Chapter 2

Chain Calculationsand

Prefix Keys

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Objectives

1. Practice various mathematical problems using chain calculations.

2. Explain the basic functionality of stack registers.

3. Practice using a prefix key to change decimal settings.

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Terms to Remember

• Chain Calculations

• Prefix Keys

• Stack Registers

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What are Chain Calculations?

• A chain calculation results when an arithmetic problem using two numbers is extended into an additional calculation.

• The HP-12C is especially efficient with chain calculations and allows the results of two calculations to be combined into a final solution with a simple keystroke.

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Chain Calculation Example

• An appraiser needs to calculate the gross living area of a house that consists of a one-story dwelling measuring 38’ x 52’, with a one-story addition that is 18’ x 22’.

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[CLX]

[38] [ENTER] [52] [x] (square feet of primary dwelling)

[18] [ENTER] [22] [x] (square feet of addition)

[+]

Result: 2,372.00 should be displayed. This is the total gross living area in square feet.

Try this…

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Total Gross Living Area Example

• A ranch-style house with an attached garage measures, in total, 56’ x 28’. The garage portion is 14’ x 28’. Find the gross living area of the house.

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Try this…

[CLX]

[56] [ENTER] [28] [x] (square feet of house and

garage)

[14] [ENTER] [28] [x] (square feet of garage)

[-]

Result: 1,176.00 should be displayed. This is the total gross living area of the house in square feet.

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Percentage of Gross Living Area Example

• Determine the percentage of total gross living area of a home that has a family room addition on the back. The primary portion is 62’ x 40’ including the garage and the family room addition is 16’ x 20’. 90% is considered living area.

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Try this…

[CLX]

[62] [ENTER] [40] [x] (square feet of primary portion and garage)

[16] [ENTER] [20] [x] (square feet of addition)

[+]

[90] [%]

Result: 2,520.00 should be displayed. This is the total gross living area of the home and family room addition.

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Total Gross Area of Two Parcels Example

• Find the total site area, in acres, of a subject that comprises two parcels that have been assembled. One parcel is 150’ x 200’ and the second parcel is 75’ x 200’.

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Try this…

[CLX]

[150] [ENTER] [200] [x] (square feet of 1st parcel)

[75] [ENTER] [200] [x] (square feet of 2nd parcel)

[+] (square feet of both parcels)

[43560] (square feet in an acre)

[÷]

Result: 1.03 should be displayed. This is the total site area in acres.

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Percentage of Area Example

• Determine what percentage of a residential yard is wooded. The yard measures 60’ x 50’ and a 30’ x 24’ section of this area is wooded.

Important: To obtain the correct result, the dimensions of the wooded area must be entered first.

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Try this…

[CLX]

[30] [ENTER] [24] [x] (square feet of wooded area)

[60] [ENTER] [50] [x] (square feet of yard)

[÷]

Result: 0.24 should be displayed, which means 24% of the yard is wooded.

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Cost per Square Yard Example

• Determine the cost of carpet for two rooms of a residential dwelling. One room is 10’ x 12’, and the carpet costs $30 per square yard installed. The other room is 16’ x 20’, and the carpet costs $42 per square yard installed.

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Try this…

[CLX]

[10] [ENTER] [12] [x] (square feet for 10 x 12 room)

[9] [÷] [30] [x] (carpet cost for 10 x 12 room)

[16] [ENTER] [20] [x] (square feet for 16 x 20 room)

[9] [÷] [42] [x] (carpet cost for 16 x 20 room)

[+]

Result: $1,893.33 should be displayed. This is the cost of carpeting both rooms.

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HP-12C Stack Registers

• There are four registers integrated into the HP-12C calculator, referred to as the stack registers.

• The stack registers could be thought of as storage areas that are stacked, or layered, on top of each other.

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HP-12C Stack Registers

• When a calculation is keyed in into the HP-12C calculator, the information is displayed in the X Register.

• Each time a new calculation is input and the [ENTER] key is pressed, the previous calculation moves up to the register above it.

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What are Prefix Keys?

• The gold [f] key and the blue [g] key located in the bottom row toward the left side of the keyboard are prefix keys.

• Many keys have gold text above them and blue writingon their lower face.

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Functions of the Prefix Keys

• The keys that have blue writing on their lower face have two functions each.

• Where there is gold writing above the keys, those keys have an additional third function.

• In order to engage the second or third function of a key, the matching prefix key is pressed and released before the desired key is pressed.

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Clearing the Prefix Keys

• A prefix key inadvertently pressed can be cleared without clearing everything else that has been keyed.

• Simply press the prefix key, gold [f] or blue [g], and then the clear prefix key [ENTER].

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The Decimal Point and Rounding

• The factory setting for the HP-12 calculator is two places to the right of the decimal point.

• It is simple to change the setting to display more or less places after the decimal point by pressing the gold [f] prefix key and then the corresponding number on the keyboard for the desired number of places.

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Try this…

• To set the decimal to four places, the keystrokes are:

[f] (“f” should appear in the display)

[4] (the number of decimal places)

Result: Four zeros (0.0000) should now be displayed to the right of the decimal point.

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Try this…

• To set the decimal to six places, the keystrokes are:

[f]

[6]

Result: Six zeros (0.000000) should now be displayed to the right of the decimal point.

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Setting the Decimal Pointat Various Times

• The decimal places can be changed at any time before, during, or after a calculation without fear of losing data or skewing the operation.

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Setting the Decimal Pointat Various Times Example

• A residential building lot measures 105’ x 263’. Begin by setting two decimal places.

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[f] [2] (sets the calculator to two decimal places)[CLX][105] [ENTER] (105.00 displays)[f] [4] (105.0000 displays)[263] [x] (27,615.0000 displays)[43560] [÷] (0.6340 displays as the total site area)[f] [6] (0.0633953 displays as the total site area)[f] [2] (Sets the calculator to two decimal places)

Result: 0.63 should be displayed as the total site area in acres.

Try this…

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• Various methods of performing a chain calculation.

• Basic functionality of the stack registers.

• How to use the prefix keys to change the function of other keys.

• The method for changing the number of decimal places that display.

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Chapter 2 Quiz

1. Two building parcels have been assembled. Individually, the parcels have dimensions of 80’ x 160’ and 75’ x 160’. In acres, what is the gross area of the assembled site?


Keystrokes: [CLX] [80] [ENTER] [160] [x] [75] [ENTER] [160] [x] [+] [43560] [÷]

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Chapter 2 Quiz

2. The rear yard of a residence measures 50’ x 40’ and a 16’ x 20’ section of this area is fenced. What percent of the yard is fenced?

Correct Answer: 16%

Keystrokes: [CLX] [16] [ENTER] [20] [x] [50] [ENTER] [40] [x] [÷]. The answer displays 0.16, which is 16%.

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Chapter 2 Quiz

3. Two rooms of a residential dwelling need to be carpeted. One room is 12’ x 12’, and the carpet costs $28 per square yard installed. The other room is 15’ x 17’, and the carpet costs $34 per square yard installed. What is the total cost of the carpet?

Correct Answer: $1,411.33

Keystrokes: [CLX] [12] [ENTER] [12] [x] [9] [÷] [28] [x] [15] [ENTER] [17] [x] [9] [÷] [34] [x] [+]

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Chapter 2 Quiz

4. What is the HP-12C calculator factory setting for the number of decimals places?

Correct Answer: two

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Chapter 2 Quiz

5. To clear a prefix key, you would

Correct Answer: press the prefix key and press the CLEAR PREFIX key [ENTER].

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Chapter 2 Quiz

6. A home comprises a one-story dwelling measuring 54’ x 30’ with a one-story addition that is 20’ x 24’. Find the total gross living area of the home plus the one-story addition.


Keystrokes: [CLX] [54] [ENTER] [30] [x] [20] [ENTER] [24] [x] [+]

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Chapter 2 Quiz

7. An L-shaped ranch dwelling, including a porch and a garage, consists of a portion that is 38’ x 30’ and a portion that is 18’ x 20’. The appraiser has determined that 80% of the structure is considered living area. What is the gross living area?


Keystrokes: [CLX] [38] [ENTER] [30] [x] [18] [ENTER] [20] [x] [+] [80] [%]

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Chapter 2 Quiz

8. Which stack register displays entries on the HP-12C calculator?

Correct Answer: X Register

The stack consists of 4 registers with the X Register entry in the display of the calculator.

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Chapter 2 Quiz

9. Which key on the HP-12C must first be pressed to change the number of decimal places?

Correct Answer: [f]

The gold [f] prefix key is pressed first, followed by the number key [0-9] of decimal places desired.

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Chapter 2 Quiz

10. Set the decimal places on your calculator to 6. Determine the number of acres of a vacant lot that measures 126’ x 42’. Change the decimal points to 5. What is displayed?


Keystrokes: [CLX] [f] [6] [126] [ENTER] [42] [x] [43560] [÷] [f] [5]

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Chapter 3

Data Storage Registersand

Percentage Problems

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Objectives

1. Practice using the storage and recall functions of the HP-12C.

2. Exhibit how to clear one or all registers.

3. Solve typical appraisal percentage problems.

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Terms to Remember

• Loan-to-value (LTV)

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Storage and Recall Functions

• The HP-12C uses data storage registers for storage and recall functions. The calculator’s storage/recall function employs the use of the storage key (STO) and the recall key (RCL).

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Storage and Recall Functions

• Appraisers can store and re-use frequently used numbers (square feet in an acre, etc.).

• The HP-12C has 20 data storage registers: – The first ten data storage registers are named

R0 through R9.– The second set is named R.0 through R.9.

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Storing Numbers in Registers

The keystrokes for storing a number in adata storage register are:

1. Input the number to be stored.

2. [STO] or [STO] [.] (depending on which set you choose).

3. Storage register.

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Storing Numbers in Registers

• To store numbers in the first set of registers, press [STO] and the storage register you wish (0-9).

• To store a number in the second set of registers, press [STO] [.] and the storage register you wish (0-9).

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• An appraiser needs to store the land area contained in a township section (640 acres).

First, set the decimal to two places.

Storing Numbers in Registers Example

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[f] [2] (sets the decimal to two places)[640] [STO] [0] (640 is stored in R0)

Result: 640.00 should be displayed. This number is stored for future use.

Try this…

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Try this…

• To recall a previously stored number, the keystrokes are:

[CLX]

[RCL] [0]

You should see that the number 640 is stored for future use.

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• To store the number of square feet in an acre (43,560) in data storage register 1, the keystrokes are:

[43560] [STO] [1] (43560 is stored in R1)

Try this…

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Calculating with Stored Numbers Example

• An appraiser is seeking to find the number of square feet contained in 1/4 of a township section comprising 640 acres.

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[CLX]

[RCL] [0] (640.00 displays)

[4] [÷] (160.00 displays, 1/4 of township in acres)

[RCL] [1] (43560.00 stored in R1, square feet in an acre)

[x]

Result: 6,969,600.000 should be displayed as the total site area in square feet.

Try this…

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• A farm comprises 720 acres. Rounded to two places, what percent of the farm section is 40 acres?


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[f] [2][CLX][720] [STO] [2] (720 stored in R2)[40] [ENTER] (40 acre section)[RCL] [2] (720.00 displays)[÷]

Result: .06 should be displayed, which is a 6% section of the farm.

Try this…

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• Determine how many acres are in a land parcel that contains 83,645 square feet, rounded to six places.


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[f] [6][CLX][83,645] [ENTER] (total square feet of parcel)[RCL] [1] (43560.000000 displays)[÷]

Result: 1.920225 should be displayed as the number of acres in the parcel.

Try this…

114

• Rounding to two places, calculate the number of cubic yards of concrete for a concrete slab 120’ x 56 ‘ and 6” thick.


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[f] [2][CLX][27] [STO] [3] (27 is stored in R3][120] [ENTER] (120’ length)[56] [x] (56’ width)[0.50] [x] (6” thickness)[RCL] [3] (27.00 displays)[÷]

Result: 124.44 should be displayed as the number of cubic yards needed.

Try this…

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Clearing One or More Registers

• To clear only one register, store “0” in that register.

• To replace a stored number, enter a different number into that register:

[RCL] [0] (640.00 displays)

[40]

[STO] [0] (40.00 should now display)

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• To clear all registers:

[f]

[CLX] (notice that the [CLX] key has “REG” above it in gold letters)

Caution: Be careful when using [f] [CLX] as this clears ALL registers!

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• To check that the registers are cleared:

[RCL] [0]

[RCL] [1]

Important: All the data storage registers must be cleared for the purpose of the National Uniform Appraiser Examination.

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The Percent Keys

• Three percentage keys.

• The percent difference key [∆%], is used for determining the percent of difference between two numbers.

120

The Percent Keys

• The percent of total key [%T], is used to determine the percent of total for one component in a problem.

• Enter as a whole number, not as a fractional derivative (e.g., 10 not .10).

121

Try this…

• To find 40% of 120, the keystrokes are:

[CLX][120] [ENTER][40][%] Result: 48.00 should be displayed.

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Net Amount

• Net amount is the base amount plus or minus the percentage amount.

• As an example, you can determine the amount of seller-paid financing concessions as a percentage and also the adjusted sale price.

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Net Amount Example

• Consider a transaction in which a house is selling for $150,000. The seller is paying 3.5% of the sale price toward the buyer’s costs. Determine the net amount.

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[CLX][150000] [ENTER][3.5] [%][-]

Result: 144,750.00 should be displayed. This is the net sale price.

Try this…

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Percent Difference

• Appraisers often need to find the difference between two sale prices for determining adjustments for market conditions and other factors.

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Percent Difference Example

• A house that sold one year ago for $300,000 sold again today for $360,000. Determine the percent difference in value.

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[CLX][300000] [ENTER][360000][∆%]

Result: 20.00 should be displayed indicating that the difference is 20%.The number appears as a positive so the percentage is also positive.

Try this…

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• Reverse the situation where the house is in a declining market. It sold one year ago for $360,000 and sold today for $300,000. Determine the percent difference in value.

Percent Difference Example

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[CLX] [360000] [ENTER] [300000][∆%]

Result: This time, the calculator is figuring the downward trend as a percent of $360,000. So, correctly input, the downward percent should be -16.67%.

Try this…

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Percent of Total Example

• A property sold for $145,000. The buyer obtained an $80,000 first mortgage from a bank and the seller held a $20,000 second mortgage. The remainder of the sale price was paid by the buyer in cash. What percent of the sale price were the mortgages in the transaction (LTV)?

Note: For a computation such as this, changing the decimal place to at least six places is advisable.

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[f] [6] (changes the decimal setting to six places) [CLX][145000] [ENTER] (sale price of home)[80000] (buyer’s first mortgage)[%T] (55.172414 percent of total)[STO] [4] (stores 55.172414 in R4)[CLX] (clears the 145,000, which is still in the

stack register)


Try this…

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[20000] (buyer’s second mortgage held by seller)

[%T] (13.793103 percent of total)

[STO]

[+]

[4] (adds 13.793103 to stored amount in R4)

[RCL] [4] (Recalls combined percent of total stored in R4)

Result: 68.965517 should be displayed. This is the percent of mortgage amount to the total sale price of the home.

Try this…

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• How to store and recall numbers in the data storage registers.

• How to clear the registers.• How to perform simple percentage calculations.• How to determine a percent of difference.• The method for determining the percent of total.• Additional uses of the [STO] and [RCL] keys.


134

Chapter 3 Quiz

1. Set data storage register R0 to 43560, the number of square feet in an acre. A land parcel contains 112,795 square feet. Rounded to six places, how many acres does the parcel contain?


Keystrokes: [43560] [STO] [0] [f] [6] [CLX] [112795] [ENTER] [RCL] [0] [÷]

135

Chapter 3 Quiz

2. Set data storage register R1 to 27, the number of cubic feet in a cubic yard. Rounding to a whole number, how many cubic yards of concrete will be needed for a concrete slab 100’ x 42’ and 6 inches thick?

Correct Answer: 78

Keystrokes: [27] [STO] [1] [f] [0] [CLX] [100] [ENTER] [42] [x] [0.50] [x] [RCL] [1] [÷]

136

Chapter 3 Quiz

3. Rounding to a whole number, what is the net sale price of a home in which the house is selling for $175,000 and the seller is paying 3% of the sale price toward the buyer’s costs?


Keystrokes: [f] [0] [CLX] [175000] [ENTER] [3] [%] [-]

137

Chapter 3 Quiz

4. Which statement regarding storage registers is false?

Correct Answer: The HP-12C contains 10 storage registers.

Actually, the HP-12C contains 20 storage registers.

138

Chapter 3 Quiz

5. A property recently sold for $328,900 and the seller carried a first mortgage of $306,000. What was the percent of the mortgage (LTV)? Round your answer to six places.

Correct Answer: 93.037397%

Keystrokes: [f] [6] [CLX] [328900] [ENTER] [306000] [%T]

139

Chapter 3 Quiz

6. Set data storage register R2 to 640, which is the

number of acres in a township. Rounded to the nearest percent, what percent of the township section is 80 acres?

Correct Answer: 13%


140

Chapter 3 Quiz

7. Set data storage register R0 to 43560, the number of square feet in an acre. A land parcel contains 142,897 square feet. Rounded to six places, how many acres does the parcel contain?



141

Chapter 3 Quiz

8. Calculate the net sale price of a home in which the house is selling for $235,000 and the seller is paying 3.5% of the sale price toward the buyer’s costs. Round your answer to a whole number.


Keystrokes: [f] [0] [CLX] [235000] [ENTER] [3.5] [%] [-]

142

Chapter 3 Quiz

9. Rounding to a whole number, what is the net sale price of a home in which the house is selling for $185,900 and the seller is paying 2.5% of the sale price toward the buyer’s costs?


Keystrokes: [f] [0] [CLX] [185900] [ENTER] [2.5] [%] [-]

143

Chapter 3 Quiz

10. Verification of a recent sale of a property for $205,000 has revealed that the seller carried a first mortgage of $155,000. What was the percent of the mortgage (LTV)? Round your answer to six places.

Correct Answer: 75.609756%

Keystrokes: [f] [6] [CLX] [205000] [ENTER] [155000] [%T]

144

Chapter 4

Time Value of Money Functions

145

Objectives

1. Describe the concept of the Time Value of Money.

2. Describe the six functions of a dollar.

3. Identify the financial register keys and explain the function of each.

4. Practice computations using the financial registers.

146

Terms to Remember

• Amortization

• Annuity

• Annuity in Advance

• Compound Interest

• Discounting

147

What is the Time Value of Money?

• Time value of money (TVM) is the concept that a dollar today is usually worth more than receiving a dollar at some point in the future.

• Time value of money functions reflect the six basic ways that money, time, and rates are tied together, known as the six functions of a dollar.

148

Six Functions of a Dollar

The six functions of a dollar are:

1. Future value of $1

2. Future value of $1 per period (annuity)

3. Sinking fund factors

4. Present value of $1 (reversion)

5. Present value of $1 per period (annuity)

6. Payment to amortize $1 (amortization)

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• The six functions of a dollar are based on the theory of compound interest.

• Compound interest is interest paid on previously earned interest based on the original principle amount.

• The more frequent the compounding period and the higher the effective interest rate, the greater the impact on the calculation.


150

• Before the availability of financial calculators, long-hand math was used for solving compound interest calculations, and later, tables were published with limited specified interest rates.

• The advantage of the HP-12C is there are no limitations to the interest rate or number of compounding periods.


151

Financial Registers

• The financial register keys are located on the left side of the top row on the HP-12C calculator:

[n] = Term or periods

[i] = Rate or interest rate

[PV] = Present value

[PMT] = Payment

[FV] = Future value

152

Financial Registers

• On the lower face of the [n] key, in blue text, “12x” appears.

• On the lower face of the [i] key, “12÷” appears in blue text.

• The blue prefix key [g] is pressed before pressing one of these keys whenever the term is in monthly periods and the amount of interest being earned will change with each deposit.

• It is very important that the frequency of compounding is consistent with the periodic interest rate.

153

Future Value of $1

• The future value of $1 is an economic concept regarding the amount of money that an investment (either a single payment or an annuity), at a fixed interest rate, for a specified period of time, will grow to in the future.

154

Future Value of $1

• The concept assumes all monies earned (interest) are reinvested.

• Works like a bank savings account.

• One should be determine that the deposit is made one time, and that the interest is not experiencing any changes during the deposit period.

155

Future Value of $1

156

Future Value of $1

• To calculate future value (FV), you need to know the:

1. Original amount of investment (present value) [PV];

2. Interest rate [i]; and

3. Length of investment term (number of periods) [n].

157

Future Value of $1 Example

• An investor puts $100 into a savings account. This represents the initial investment amount, or present value [PV].

• The bank pays 6% interest, which is the interest rate [i]. By using simple math, after one year, the investment will have a future value of $106 ($100 x 1.06 = $106).

• How much will the investment have at the end of the second year ?

158

Important Points to Consider

• For all compounding problems, the display should be set at least six places past the decimal.

• Most errors in these types of calculations stem from NOT having the calculator properly cleared.

• Other than the first keystrokes to clear the registers and the last keystroke, there is no particular order that needs to be followed when inputting data.

159

Try this…

[n] = 2; [i] = 6; and [PV] = $100

[f] [CLX] (clears all registers)[f] [6] (sets the decimal to 6 places)[2] [n] (term of two years)[6] [i] (interest rate of 6%)[100] [PV] ($100 initial deposit)[FV]

Result: -112.360000 should be displayed, or $112.36.

160

Important Note

• The HP-12C processes data in terms of cash flows.

• Hence, the $100 going into the bank is a positive cash flow for the bank.

• At the end of the term when the principal and interest are returned, the cash going out of the bank is considered a negative cash flow.

161

Future Value of $1 Per Period (Annuity)

• Future value of $1 per period is an economic concept that demonstrates what $1 invested on a periodic basis (e.g., weekly, monthly, yearly) will grow to if the investment is allowed to grow over time and all interest is reinvested (compounded).

• This is also known as an annuity.

162


• This function works very much like the future value of $1 except, rather than placing a single payment into an account at the beginning of the term, payments are deposited on a regular or periodic basis at the end of the term.

• A periodic payment placed in an account at the beginning of the period is called an annuity in advance.

163


164

Begin and End Keys

• This is where the [BEG] and [END] keys are used.

• These keys are located on the lower face of the 7 and 8 number keys.

• Notice that the text is in blue; therefore, the blue [g] prefix key must be pressed before pressing one of these keys.

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Begin and End Keys

• The default setting of the HP-12C is for the end of the term.

• If the payment is at the beginning of the term, such as in an absolute net lease due at the first of each month, the calculator must be set for a “beginning term” calculation by pressing [g] [BEG].

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• To calculate future value of $1 per period (FV), you need to know the:

1. Payment to be invested each period (PMT);


3. Length of investment term (number of periods) [n].

Future Value of$1 Per Period (Annuity)

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Future Value of $1 Per Period (Annuity) Example

• After paying all expenses on a building, an investor will have $100 at the end of each year to deposit into a savings account. This represents the periodic payment [PMT].

• The bank pays 6% interest, which is the interest rate [i].

• Note that after the first year, the investment will have a future value of only $100, since the money was just placed in the account.


168


• At the end of year two, the total amount grows to $206.

• The first $100 deposit has now earned $6 interest and an additional $100 is added at the end of the second year.

• This amount will grow at 6% for the next year and equal $218.36 at the end of that time — at which time another $100 is deposited, bringing the total to $318.36 for three years [n].

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Try this…

[n] = 3, [i] = 6, and [PMT] = $100

[f] [CLX] (clears all registers)[3] [n] (term of three years)[6] [i] (interest rate of 6%][100] [PMT] ($100 payment to be invested each

period)[FV]

Result: -318.360000 should be displayed, or $318.36.

170

• After paying all expenses on a building, an investor will have $50 each month to deposit into a savings account.

• The interest rate is 6%.

• What will the balance be after three years of deposits?


171

Try this…

[n] = 3; [i] = 6; and [PMT] = $50

[f] [CLX][3] [g] [n] (3 years converted to a monthly basis)[6] [g] [i] (6% interest converted to a monthly basis)[50] [PMT] ($50 payment to be deposited each month)[FV]

Result: -1,966.805248 should be displayed, or $1,966.81.

172

Sinking Fund Factor

• The sinking fund factor is an economic concept regarding an amount of money set aside on a periodic basis so that, when compounded at a given interest rate for a defined term, it will accumulate to a specified future sum.

173

Sinking Fund Factor

• Sinking fund factors show the amount of regular payments that must be invested over a period of time at a specified interest rate, with reinvestment of all monies earned, so a target amount is accumulated at the end of the term.

174

Sinking Fund Factor

• To calculate sinking fund factors, you need to establish:

1. The future value (target amount) [FV];

2. When the final amount is needed, or after how many intervals [n];

3. How often contributions will be made (monthly, annually) [PMT]; and

4. The interest rate it will earn over time [i].

175

Sinking Fund Factor Example

• An investor needs $1,000 at the end of 10 years.

• If the investment will earn 6% interest, how much must the investor deposit every year over the 10 years to end up with exactly $1,000?

176

Try this…

[n] = 10; [i] = 6; and [FV] = $1,000

[f] [CLX][10] [n] (term of ten years)[6] [i] (interest rate of 6%)[1000] [FV] ($1,000 future value)[PMT]

Result: -75.867958 should be displayed, or $75.87 each year. $758.70 + compound interest = $1,000.

177

Try this…

Monthly deposit keystrokes:

[f] [CLX][10] [g] [n] (10 years converted to monthly)[6] [g] [i] (6% interest converted to monthly)[1000] [FV] ($1,000 future value)[PMT]

Result: -6.102050 should be displayed, or $6.10 each month.

178

Present Value of $1 (Reversion)

• Present value is an amount today that is equivalent to a future payment, or a series of payments (annuity), based on a specified interest rate, for a specific period of time.

• The present value of $1 is an economic concept that demonstrates how much must be invested today for the investment to grow to $1 at the end of a specified time period, with reinvestment of all monies earned.

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• Amount of future value is known.• Determine how much money (present value)

invested today, with compound interest, is required to reach a specified amount in the future.

• Think of present value as the opposite function of future value.

• Investors sometimes refer to converting monies due in the future to present value as discounting.

180


• Present value is often abbreviated PV.To calculate PV, you need to establish:

1. The amount to be received in the future [FV];

2. The required interest rate the investment will

earn [i]; and

3. When in the future the amount is scheduled to be received (term) [n].

181

Present Value of $1 (Reversion) Example

• A promissory note for $1,000 is due in two years. A typical return on deposits is currently 8% annually with monthly compounding. How much is the note worth today?

Important: The term and rate will be converted to a monthly basis using the blue [g] prefix key. Annual compounding would omit this keystroke.

182

Try this…

[n] = 2; [i] = 8; and [FV] = $1,000

[f] [CLX][2] [g] [n][8] [g] [i][1000] [FV][PV]

Result: -852.596376 should be displayed, or $852.60

183

Present Value of $1 Per Period (Annuity)

• Present value of $1 per period (annuity) is an economic concept that demonstrates how much money, in a single payment, must be invested today and compounded into the future to equal a series of periodic payments in the future.

• An amount of money in the future is known, but, rather than it being a single amount, it is a series of equal payments received in the future on a periodic basis (e.g., weekly, monthly, yearly).

184

• Present value of $1 per period uses the same abbreviation as present value (PV).

• To calculate, you need to know the:

1. Amount being received each period [PMT];


3. Length of the investment term [n].

Present Value of $1 Per Period (Annuity)

185

Present Value of $1 Per Period (Annuity) Example

• A land contract will pay $1,000 per month for the next five years. If a potential purchaser of this land contract would like to make 8% interest on the investment, how much is the land contract worth in present value?

186

Try this…

[n] = 5; [i] = 8; and [PMT] = $1,000

[f] [CLX][5] [g] [n][8] [g] [i][1000] [PMT][PV]

Result: -49,318.43334 should be displayed, or a present value of $49,318.43.

187

Payment to Amortize $1

• Amortization is elimination of a debt with a series of equal payments (principle and interest) at regular time intervals.

• When a loan is fully amortized, the total payments retire the entire balance of principal and interest at the end of the loan term.

188


• The objective is to take a principal loan amount and determine the payment amount required to repay both the principal and all interest due over the life of the loan.

• Same concept as a fixed-rate, fixed term home mortgage.

Note: This calculation will NOT work for variable-rate or variable-term loans.

189

• To calculate the payment needed to amortize a loan, you must determine the:

1. Amount borrowed [PV];


3. Length of the loan term [n].

Note: Generally, loan payments are made monthly, but may be make weekly, quarterly, or annually.


190

Payment to Amortize $1 Example

• A homeowner has a $100,000, 30-year mortgage at 6% interest. What are the monthly payments?

191

Try this…

[n] = 30; [i] = 6; and [PV] = $100,000

[f] [CLX][30] [g] [n][6] [g] [i][100000] [PV][PMT]

Result: -599.550525 should be displayed, or a monthly payment of $599.55.

192


• The concept of the Time Value of Money (TVM).

• The six functions of a dollar.

• The functions of the financial register keys.

• How to solve equations using the financial registers.

193

Chapter 4 Quiz

1. Rounding your answer to the nearest cent, if $750 is deposited in a savings account earning 11.50% interest, how much will be in the account at the end of 3 years?


Keystrokes: [f] [CLX] [750] [PV] [11.5] [i] [3] [n] [FV]

194

Chapter 4 Quiz

2. A heating system will need to be replaced in 10 years at a cost of $16,000. To have enough set aside when the replacement is necessary, what amount will need to be deposited monthly if the account will earn 2.5% interest? Round your answer to the nearest cent.

Correct Answer: $117.50

Keystrokes: [f] [CLX] [16000] [FV] [10] [g] [n] [2.5] [g] [i] [PMT]

195

Chapter 4 Quiz

3. What is the current value of $25,000 discounted at 11%, due in one year? Round to the nearest whole dollar.

Correct Answer: $22,523

Keystrokes: [CLX] [25000] [FV] [11] [i] [1] [n] [PV]

196

Chapter 4 Quiz

4. The monthly debt service on a loan is $1,608.52. If the interest rate for the loan is 6.75% for a 30-year term, what was the original loan amount? Round your answer to the nearest thousand.


Keystrokes: [f] [CLX] [1,608.52] [PMT] [6.75] [g] [i] [30] [g] [n] [PV]

197

Chapter 4 Quiz

5. Rounding your answer to the nearest cent, what is the monthly debt service on a 30-year mortgage loan at 5.5% interest if the beginning principal balance is $92,000?


Keystrokes: [CLX] [92000] [PV] [5.5] [g] [i] [30] [g] [n] [PMT]

198

Chapter 4 Quiz

6. Rounding your answer to the nearest cent, if $1,250 is deposited in a savings account earning 5.25% interest, how much will be in the account at the end of 5 years?


Keystrokes: [f] [CLX] [1250] [PV] [5.25] [i] [5] [n] [FV]

199

Chapter 4 Quiz

7. Rounding your answer to the nearest cent, if $30 is deposited each month for a period of 6.5 years, what will the balance be in a savings account earning 3.25 percent interest?


Keystrokes: [f] [CLX] [30] [PMT] [6.5] [g] [n] [3.25] [g] [i] [FV]

200

Chapter 4 Quiz

8. An investment property owner wants to ensure that he has enough funds set away to replace these capital items in 15 years: Furnace - $18,500; Roof - $17,000. How much must be deposited each month in an account bearing 4% interest? Round your answer to the nearest cent.


Keystrokes: [f] [CLX] [18500] [ENTER] [17000] [+] [FV] [15] [g] [n] [4] [g] [i] [PMT]

201

Chapter 4 Quiz

9. Rounding your answer to the nearest cent, what is the current value of $100,000 compounded monthly for 10 years at 8% interest?


Keystrokes: [f] [CLX] [100000] [FV] [10] [g] [n] [8] [g] [i] [PV]

202

Chapter 4 Quiz

10. Over the next five years, a land contract pays $400 payments at the end of each month. If an investor wanted to make a 10% return on investment, what is the value today of the land contract? Round your answer to a whole dollar.


Keystrokes: [f] [CLX] [400] [PMT] [5] [g] [n] [10] [g] [i] [PV]

203

Chapter 5

Net Present Valueand

Internal Rate of Return

204

Objectives

1. Explain cash inflows and cash outflows.

2. Practice calculating net present value and internal rate of return.

3. Determine whether or not to accept or reject a project or investment.

205

Terms to Remember

• Cash Flow

• Discounting

• Internal Rate of Return (IRR)

• Net Present Value (NPV)

206

Cash Flows

• Cash flow is a revenue or expense stream that changes a cash account over a given period.

• Cash inflows usually arise from financing, operations, or investing.

• Cash outflows result from expenses or investments.

• Often a project or investment will contain several different cash flows.

207

Cash Flows Example

• You have an investment opportunity for an office building. The initial purchase price is $200,000. You expect to receive the following rents over the first five years.

208

Cash Flows Example

• Cash outflows are shown as negative values (money paid out). Cash inflows are shown as positive values (money received).

209

What is Net Present Value (NPV)?

• Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows.

• Basically, NPV determines the current value of all the cash flows of a project.

• Result determines if a project should be accepted or not:– Positive result = accepted– Negative result = rejected

210

What is Net Present Value (NPV)?

• Required to make one assumption—the discount rate.

• Discounting, is the process, by some investors, that uses the principles of TVM to convert future income or cash flows into present value, at a specified interest rate.

• Typically, the cost of capital is used for discounting.

211

NPV Keys and Functions

• [FIN] Clears all financial registers

• [CFo] Initial Cash Flow ($)

• [CHS] Change Sign

• [CFj] Incremental Cash Flow ($)

• [Nj] Number of periods that incremental

cash flows repeats (#)

• [NPV] Calculate Net Present Value

212

Use Prefix Keys with NPV Keys

• Use either the gold [f] prefix key or the blue [g] prefix key for each function.

• For example, press [f] before the NPV key; press [g] before the [CFo] key.

213

Points to Remember

• Initial investment is a cash flow paid out, so use the change sign key [CHS] to change that number to a negative amount.

• Can store up to 20 cash flow amounts in addition to the initial investment.

• NPV cash flows can be grouped or ungrouped. Grouped cash flows are consecutive cash flows of the same amount. Ungrouped cash flows are not.

214

Points to Remember

• Equal consecutive cash flows are entered as a number of periods followed by the [g] [Nj] keys.

• Can have up to 99 cash flows.

215

Net Present Value and Cash Flows

• One of the most important steps in the calculation of the NPV method is to accurately illustrate the cash flows and when they occur.

• Use a table or graphic to illustrate cash flows.

216

NPV and Cash Flows Example

• A project with an initial cost of $100,000 has cash inflows in years 1-3 of $20,000 and in years 4-5 of $50,000. In year 3, there is an additional cash outflow of $30,000. Cost of capital is 10%.

217


218


219

Try this…

[f] [FIN] (clears all registers)100000 [CHS] [g] [CFo] (negative initial cash flow)20000 [g] [CFj] (next cash flow)2 [g] [Nj] ($20,000 repeats 2 times)10000 [CHS] [g] [CFj] (next cash flow)50000 [g] [CFj] (next cash flow)2 [g] [Nj] ($50,000 repeats 2 times)10 [i] (10% discount rate)[f] [NPV] (calculates NPV)

Result: -7,605.665286 should be displayed, or a net present value of -$7,605.67.

220


• A project with an initial cash outflow of $500,000. Each year for the next 10 years, the project has a cash outflow of $90,000. Assume a cost of capital of 12%.

221

Try this…

[f] [FIN]500000 [CHS] [g] [CFo] (negative initial cash flow)90000 [g] [CFj] (next cash flow)10 [g] [Nj] ($90,000 repeats 10 times)12 [i] (12% discount rate)[f] [NPV] (calculates NPV)

Result: 8,520.072557 should be displayed, or a net present value of $8,520.08.

222


• Imagine a project with the following cash flows and a discount rate of 8%:

223

Try this…

[f] [FIN]1000000 [CHS] [g] [CFo] (negative initial cash flow)275000 [g] [CFj] (next cash flow)125000 [g] [CFj] (next cash flow)450000 [g] [CFj] (next cash flow)550000 [g] [CFj] (next cash flow)2 [g] [Nj] ($550,000 repeats 2 times)8 [i] (8% discount rate)[f] [NPV] (calculates NPV)

Result: 497,608.6680 should be displayed, or a net present value of $497,608.67.

224

What is Internal Rate of Return (IRR)?

• Internal rate of return (IRR) is the discount rate often used in capital budgeting that makes the net present value of all cash flows from a particular project equal to zero.

• You must make an assumption regarding your acceptable rate of return. Typically, each firm establishes a threshold for this value.

225

What is Internal Rate of Return (IRR)?

• The calculation assumes that any cash outflows generated by the project can be reinvested at the IRR.

• The calculation result is a percentage.

• A value greater than the threshold indicates that the project should be accepted; a value less than the threshold indicates that the project should be rejected.

226

• As with NPV, you must determine the yearly cash flows for project.

• Use the IRR key to obtain the result of the calculations.

Internal Rate of Return andCash Flows

227

IRR and Cash Flows Example

• Initial Outflow is $250,000; annual inflows are $65,000, and length of project is 9 years.

228

Try this…

[f] [FIN]

250000 [CHS] [g] [CFo] (negative initial cash flow)

65000 [g] [CFj] (next cash flow)

9 [g] [Nj] ($65,000 repeats 9 times)

[f] [IRR] (calculates IRR)

Result: 21.491060 should be displayed, or an internal rate of return of 21.49%.

Note: The IRR function displays “running” while the answer is being calculated.

229


• Initial Outflow is $340,000; annual inflows are $72,000, and length of project is 10 years.

230

Try this…

[f] [FIN]



10 [g] [Nj] ($72,000 repeats 10 times)


Result: 16.628688 should be displayed, or an internal rate of return of 16.63%.

231


• A project requires an initial investment of $450,000 with an additional investment in year 4. The cash flows are:

232


• At the end of the project, you will be able to sell the assets for an additional $100,000. Your required return is 15%. Should you accept the project?

233

Try this…

[f] [FIN]





100000 [CHS] [g] [CFj] (next cash flow)





234

Try this…

Result: An “Error 3” message displays, which means that there are possibly multiple IRRs.

• You can still create the calculation, but you need to give the calculator an estimate of the answer.

• Use the pause key [PSE] to interrupt the program while allowing you to enter new data. The [PSE] key is located on the [R/S] key.

235

• To enter an estimate, the keystrokes are:

[CLX] <enter estimate> [i] [RCL] [g] [PSE]• Enter the required return of 15%:

[CLX] 15 [i] [RCL] [g] [PSE]

Try this…

236


• Both net present value (NPV) and internal rate of return (IRR) are good tools to use to help you evaluate investment projects through a series of cash flows.

• Net present value will return a dollar value as an answer. A positive value suggests that you should accept the project. A negative value suggests that you should reject the project.

237


• Internal rate of return will give you a percentage answer that indicates the annual yield on the project. A value greater than your required rate of return suggests that you should accept the project.

238

Chapter 5 Quiz

1. When preparing cash flow tables, the general convention is that positive values are shown as

Correct Answer: cash inflows.

239

Chapter 5 Quiz

2. An apartment complex has a purchase price of $300,000. The expected annual rental income is $60,000 for each of the ten years. Assuming a cost of capital of 12%, what is the net present value of acquiring the building? Round your answer to the nearest dollar.


Keystrokes: [f] [FIN] [300000] [CHS] [g] [CFo] [60000] [g] [CFj] [10] [g] [Nj] [12] [i] [f] [NPV]

240

Chapter 5 Quiz

3. You can purchase a duplex for $175,000. The expected annual rental income is $24,000 for each of the next fifteen years. Assuming you can obtain financing at 9%, what is the NPV of the investment? Round your answer to the nearest dollar.



241

Chapter 5 Quiz

4. You can purchase a small strip mall for $150,000. The expected annual rental income is $30,000 for each of the next six years. What is the internal rate of return for the building? Round your answer to the nearest whole percent.

Correct Answer: 5%

Keystrokes: [f] [FIN] [150000] [CHS] [g] [CFo] [30000] [g] [CFj] [6] [g] [Nj] [f] [IRR]. Actual answer is 5.47%.

242

Chapter 5 Quiz

5. You can purchase an office building for $400,000. The expected annual rental income is $100,000 for each of the next six years. What would your cost of capital need to be to accept the project? Round your answer to the nearest whole percent.

Correct Answer: 13%

Keystrokes: [f] [FIN] [400000] [CHS] [g] [CFo] [100000] [g] [CFj] [6] [g] [Nj] [f] [IRR]. Actual answer is 12.98%.

243

Chapter 5 Quiz

6. Cash flow

Correct Answer: is a revenue or expense stream that changes a cash account over a given period.

244

Chapter 5 Quiz

7. An apartment complex has a purchase price of $500,000. The expected annual rental income is $80,000 for each of the ten years. Assuming a cost of capital of 10%, what is the net present value of acquiring the building? Round your answer to the nearest dollar.

Correct Answer: -$8,435


245

Chapter 5 Quiz

8. You can purchase a duplex for $150,000. The expected annual rental income is $33,000 for each of the next twelve years. Assuming you can obtain financing at 10%, what is the NPV of the investment? Round your answer to the nearest dollar.


Keystrokes: [f] [FIN] [150000] [CHS] [g] [CFo] [33000] [g] [CFj] [12] [g] [Nj][10] [i] [f] [NPV]

246

Chapter 5 Quiz

9. You can purchase a small strip mall for $175,000. The expected annual rental income is $35,000 for each of the next eight years. What is the internal rate of return for the building? Round your answer to the nearest whole percent.

Correct Answer: 12%

Keystrokes: [f] [FIN] [175000] [CHS] [g] [CFo] [35000] [g] [CFj] [8] [g] [Nj] [f] [IRR]. Actual answer is 11.81%

247

Chapter 5 Quiz

10. You can purchase an office building for $300,000. The expected annual rental income is $95,000 for each of the next four years. What would your cost of capital need to be to accept the project? Round your answer to the nearest whole percent.

Correct Answer: 10%

Keystrokes: [f] [FIN] [300000] [CHS] [g] [CFo] [95000] [g] [CFj] [4] [g] [Nj][f] [IRR]. Actual answer is 10.17%.

248

Chapter 6

Statistical Calculations

249

Objectives

1. Practice using the HP-12C to calculate the mean and the standard deviation.

2. Demonstrate how to calculate both the mean and the standard deviation in the same problem.

250

Terms to Remember

• Mean

• Standard Deviation

251

Statistical Functions of the HP-12C

• Use the HP-12C to calculate and store statistical data in the statistical registers.

• Two most common statistical calculations are the mean and the standard deviation.

• The mean is a statistical term for the average of a set of numbers.

• The standard deviation describes how far each statistic varies from the mean.

252

Keys for Statistical Calculations

• [f] [Σ] Clears the statistical registers.

• [Σ] Controls the statistical registers.

253

Keys for Statistical Calculations

• [Σ+] Allows you to add values to the statistical registers.

• [g] [x-bar] Calculates the average or mean (x-bar is located on the 0 key).

254

The Mean

• The mean is the sum of all the data points, divided by the number of data points; or the average.

• Used by appraisers for reconciliation, adjustments, and multiple conclusions.

255

The Mean Example

• To calculate the mean of the numbers, 10, 15, 35, 25, 18, and 23, you would add all six of the numbers together to get a total of 126. Then, you would divide by 6 to get the average of 21.

• Now, using the HP-12C, calculate the mean of the numbers 10, 15, 35, 25, 18, and 23.

256

Try this…

[f] [Σ] (clears the statistical registers)10 [Σ+] (enters the first value)15 [Σ+] (enters the second value)35 [Σ+] (enters the third value)25 [Σ+] (enters the fourth value)18 [Σ+] (enters the fifth value)23 [Σ+] (enters the sixth value)[g] [x-bar or 0] (calculates mean)

Result: 21 should be displayed.

257

Number of Stored Values

Note: Each you press [Σ+], the number of values stored in the statistical registers will display. For example, after the first entry, “1” displays, after the second entry “2” displays, and so forth.

258

Try this…

• Calculate the mean for the numbers 46, 33, 17, 82, 51, 43, 61,12, 39, and 91:

[f] [Σ] (clears the statistical registers)

46 [Σ+] (enters the first value)

33 [Σ+] (enters the second value)

17 [Σ+] (enters the third value)

82 [Σ+] (enters the fourth value)


259

Try this…

51 [Σ+] (enters the fifth value)

43 [Σ+] (enters the sixth value)

61 [Σ+] (enters the seventh value)

12 [Σ+] (enters the eighth value)

39 [Σ+] (enters the ninth value)

91 [Σ+] (enters the tenth value)

[g] [x-bar or 0] (calculates mean)


260

The Standard Deviation

• The standard deviation is a measure of the dispersion of a set of data from its mean.

• Generally used by appraisers for advanced calculations and determining adjustments.

261

The Standard Deviation

• The standard deviation is strictly a measure of how spread apart your data is.

• Keystrokes for the standard deviation are [g] [s]. The [s] key is located on the decimal key [.].

262

Try this…

• Calculate the standard deviation for 10, 15, 35, 25, 18, and 23:






263

Try this…




[g] [s] (calculates standard deviation)


264

Try this…

• Calculate the standard deviation for the numbers 46, 33, 17, 82, 51, 43, 61,12, 39, and 91:







265

Try this…







[g] [s] (calculates standard deviation)


266

Calculating Both the Mean and Standard Deviation

• You can compute both the mean and standard deviation—one after the other.

• Once you enter the values in the set of numbers, press [g] [x-bar] to calculate the mean, and then press the [g] [s] keys to calculate the standard deviation.

267

Try this…

Compute both functions using the numbers 10, 15, 35, 25, 18, and 23:






268

Try this…




[g] [x-bar] (calculates mean of 21)

[g] [s] (calculates the standard deviation of

8.74)

269

Try this…

• Calculate the mean and the standard deviation for the numbers 14, 18, 12, 20, 16, and 22:







270

Try this…



[g] [x-bar] (calculates mean)

[g] [s] (calculates the standard deviation)

Result: 17 should be displayed for the mean and 3.74 should be displayed for the standard deviation.

271


• How to compute two statistical calculations using the HP-12C: The mean and the standard deviation.

• How to calculate both the mean and the standard deviation for the same problem by simply calculating the mean first, and then pressing [g] [s] for the standard deviation.

272

Chapter 6 Quiz

1. A small subdivision contains 12 homes of different floor plans. Using the following details about their square footages, calculate the mean:

1500 1485 1740 1665

1575 1450 1720 1695

1545 1530 1770 1635

Correct Answer: 1609

Keystrokes: [f] [Σ] [1500] [Σ+] [1485] [Σ+] [1740] [Σ+] [1665] [Σ+] [1575] [Σ+] [1450] [Σ+] [1720] [Σ+] [1695] [Σ+] [1545] [Σ+] [1530] [Σ+] [1700] [Σ+] [1635] [Σ+] [g] [x-bar]

273

Chapter 6 Quiz

2. An apartment building has a variety of rental rates depending on the type of apartment. There are a total of four apartments in the building. Find the average rental rate based upon the data below:

1BR 2BR 3BR 2BR+Patio

$500 $650 $800 $750

Correct Answer: $675

Keystrokes: [f] [Σ] [500] [Σ+] [650] [Σ+] [800] [Σ+] [750] [Σ+] [g] [x-bar]

274

Chapter 6 Quiz

3. A small subdivision contains 12 homes of different floor plans. Using the following details about their square footages, calculate the standard deviation:

1500 1485 1740 1665

1575 1450 1720 1695

1545 1530 1770 1635


Keystrokes: [f] [Σ] [1500] [Σ+] [1485] [Σ+] [1740] [Σ+] [1665] [Σ+] [1575] [Σ+] [1450] [Σ+] [1720] [Σ+] [1695] [Σ+] [1545] [Σ+] [1530] [Σ+] [1700] [Σ+] [1635] [Σ+] [g] [s]

275

Chapter 6 Quiz

4. Eight homes have sold within the past few months. Before you start your appraisal work, find the standard deviation:

$150,000 $165,000 $148,000 $142,000

$156,000 $163,000 $170,000 $159,000


Keystrokes: [f] [Σ] [150000] [Σ+] [165000] [Σ+] [148000] [Σ+] [142000] [Σ+] [156000] [Σ+] [163000] [Σ+] [170000] [Σ+] [159000] [Σ+] [g] [s]

276

Chapter 6 Quiz

5. Six homes have sold within the past few months. Before you start your appraisal work, find the mean sales price, and then find the standard deviation:

$150,000 $165,000 $148,000

$156,000 $163,000 $170,000

Correct Answer: $158,667, $8,756

Keystrokes: [f] [Σ] [150000] [Σ+] [165000] [Σ+] [148000] [Σ+] [156000] [Σ+] [163000] [Σ+] [170000] [Σ+] [g] [x-bar] [g] [s]

277

Chapter 6 Quiz

6. A small subdivision contains 8 homes of different floor plans. Using the following details about their square footages, calculate the mean:

2250 2175 2060 2235

2190 2145 2095 2270


Keystrokes: [f] [Σ] [2250] [Σ+] [2175] [Σ+] [2060] [Σ+] [2235] [Σ+] [2190] [Σ+] [2145] [Σ+] [2095] [Σ+] [2270] [Σ+] [g] [x-bar]

278

Chapter 6 Quiz

7. An apartment building has a variety of rental rates depending on the type of apartment. There are a total of four apartments in the building. Find the average rental rate based upon the data below:

1BR 2BR 3BR 2BR+Patio

$650 $750 $900 $850


Keystrokes: [f] [Σ] [650] [Σ+] [750] [Σ+] [900] [Σ+] [850] [g] [x-bar]

279

Chapter 6 Quiz

8. A small subdivision contains 8 homes of different floor plans. Using the following details about their square footages, calculate the standard deviation:

2250 2175 2060 2235

2190 2145 2095 2270


Keystrokes: [f] [Σ] [2250] [Σ+] [2175] [Σ+] [2060] [Σ+] [2235] [Σ+] [2190] [Σ+] [2145] [Σ+] [2095] [Σ+] [2270] [Σ+] [g] [s]

280

Chapter 6 Quiz

9. Five homes have sold within the past few months. Before you start your appraisal work, find the standard deviation:

$220,000 $235,000 $246,000 $251,000$234,000


Keystrokes: [f] [Σ] [220000] [Σ+] [235000] [Σ+] [246000] [Σ+] [251000] [Σ+] [234000] [Σ+] [g] [s]

281

Chapter 6 Quiz

10. Five homes have sold within the past few months. Before you start your appraisal work, find the mean sales price, and then find the standard deviation:

$233,000 $259,000 $248,000 $210,000$225,000

Correct Answer: $235,000, $19,196

Keystrokes: [f] [Σ] [233000] [Σ+] [259000] [Σ+] [248000] [Σ+] [210000] [Σ+] [225000] [Σ+] [g] [x-bar] [g] [s]

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