Exam 1 Review

Things You Should Know

Time Value of Money problems

All the readings including WSJ ‘little’ book Stocks: trading, calculating returns Mutual Funds Stock Indexes

TVM How to work your calculator

Setting different compounding periods

PV and FV of single cash flow

PV and FV of multiple cash flows Annuities Annuities due Perpetuities

Translating word problems into TVM

TVM

Finding the single unknown PV, FV, N, I/YR, PMT

Different ways of stating interest rates APR, EAR, Add-on, Points

Combining PV and FV problems Saving for retirement

Comparing different choices using TVM e.g. Lease vs. Buy

TVM Problems

Five main keys: PV FV PMT I/YR N

Setting Key: P/YR

Before you begin TVM Read the problem and determine

compounding period

Find out what is asked

Check and set P/YR and BEG/END keys

Clear all memory

Example 1

First Simple Bank pays 6% compounded quarterly whereas First Complex Bank pays 6% compounded continuously. You deposit $15,000 for 3 years in each bank, which account will have more and by how much more?

Answer: $23.98

Example 1 (contd.)

What are the EARs on the two accounts?

Answer: Quarterly: 6.13% Answer: Continuously: 6.18%

Note:

When you have continuous compounding problem, you must use the formula (unless your calculator has continuous compounding function - e.g. 17B)

When you use any formula, enter interest rate in decimals!

Example 2

At 9% interest rate compounded monthly, how many years does it take to quardruple your money?

Answer: 15.46 years

Example 3

You are scheduled to receive $17,000 in two years. When you receive it, you will invest it for six more years at 6 percent per year. How much will you have in eight years?

Answer: $24,114.82

Example 4 Calculate the interest rate charged by a

car dealer when you buy a $14,000 car and are asked to make $349 monthly payments for four years.

Answer: 9.09% per year APR

What is the EAR on the loan? Answer: 9.48% EAR

Example 5

You make 12 monthly payments of $500 starting immediately into an account that earns 8.5% APR compounded monthly. How much will you have at the end of the year?

Answer: $6,283.55

Example 6

Credit card co’ offers 6.9% per year for first 6 months and 22% thereafter, both compounded monthly. You transfer $3,000 balance. How much interest will you owe at the end of the first year?

Answer: $462.59

Example 7 Calculate the interest, principal of your last

payment and balance owed on a 30-year, $325,000 mortgage after you have made monthly payments for 23 years. Interest is 11% APR compounded monthly.

Answers:Interest: $1,670.03Principal: $1,425.02Balance: $180,760.02

Example 8 Your friend is celebrating 35th birthday

and wants to retire at age 65. She wants to withdraw $10,000 on each birthday for 15 years in retirement. A credit union offers 11% per year interest.How much must she deposit every year?

Answer: $361.31

Example 8 continued

If she just inherited money and wants to make one lumpsum deposit today, what amount must she deposit?

Answer: $3,141.17

Example 8 (contd.)

Your friend’s employer will contribute $100 every year. Also, she expects $15,000 from family trust on her 55th birthday which she will put into retirement a/c. What amount must she deposit annually to meet her goals?

Answer: $47.31

Example 9

A check cashing store makes a 1-year ‘discount’ loan of $12,000 by deducting interest at 13% per year immediately. Interest deducted: 12,000 * .13 = $1,560You get: 12,000 - 1,560 = $10,440

What is the EAR on the loan? Answer: 14.94%

Example 10

What is the APR and EAR on a 10-year, $170,000 monthly payment loan quoted as 9% + 2 points?

Answers: APR = 9.47% EAR = 9.89%