Rounding in MyFinanceLab In MyFinanceLab we use input instructions to indicate the place value to which you must round your final answer(s). For example: Let’s say our final answer is 736.2359.

• You should enter 736.2 if the input instruction is: Round to the nearest tenth. • You should enter 736.24 if the input instruction is: Round to the nearest

hundredth. (Or Round to the nearest cent if the final answer is in currency units) • You should enter 736.236 if the input instruction is: Round to three decimal

places. Now, let’s use a simple Time Value of Money (TVM) question you may encounter in MyFinanceLab. Comparing Interest for Various Compounding Periods. If $1,000 is invested at 8% compounded

a. annually, b. monthly,

what is the amount after 5 year? (Round to the nearest cent.) To solve this problem without using a financial calculator or a spreadsheet, we need to use the compound interest, future value, formula: niPVFV )1( += where,

i = r/m FV = future value at the end of n periods PV = present value

r = annual rate m = number of compounding periods per year i = rate per compounding period n = Total number of compounding periods

Solution:

a. Compounding annually means that there is one interest payment period per year. So, n = 5 and i = r = 0.08.

niPVFV )1( += 5)08.01(000,1 +=FV

3280768.469,1)4693280768.1(000,1

=

=

FVFV

Therefore, rounded to the nearest cent, the final answer is $1,469.33

b. Compounding monthly means that there are twelve interest payments per year. So, n = 12(5) = 60 and i = 0.08/12 = 600666.0

niPVFV )1( +=

8457086.489,1)4898457086.1(000,1

1208.01000,1

60

=

=

⎟⎠

⎞⎜⎝

⎛ +=

FVFV

FV

Therefore, rounded to the nearest cent, the final answer is $1,489.85 This TVM example helps us to understand a basic rounding principles in MyFinanceLab: “Do not round until the final answer.” As you can see in part a. after solving the expression ( )508.01+ we leave it unrounded and use as many digits as possible in its decimal part. The same happens in part b with the other exponential expression. Take another look at part b. because rounding i to a small number of decimal places, such as 0.007 or 0.0067, would have resulted in round-off errors. So, to avoid this, use as many decimal places as your calculator is capable of displaying. Tips: If you want to calculate TVM problems, mathematical calculations are relatively straightforward. However, as you will see, TVM calculations are easier using a financial calculator or spreadsheet. But, no matter what method you use – equation, financial calculators, or spreadsheets, you get the same answer because they all use the same formula and concept. These are some tips for solving TVM questions. Calculator Tips:

• Set your calculator to display at least five decimal places or to floating decimal place (nine decimal places).

• Set your calculator to one payment per year. Adjust this setting if necessary. • Set your calculator to the “end” mode. Adjust this setting if necessary.

Excel Tips: • Take advantage of the formula help that Excel offers. • If you are lost, click on ”Help.” • Be careful about rounding variables. For example, suppose you’re dealing with

the interest rate 6.99% compounded monthly. This means you will need to enter the interest rate per month, which is = 6.99%/12, and since you are performing division in the cell, you need to put an “=” sign before the division is performed. Don’t round the result of 0.0699/12 to 0.58 and enter 0.58 as i. Instead, enter =6.99%/12 or as a decimal =0.0699/12 for i.