Chapter 4

When your father was born 44 years ago, his grandparents deposited $100 in an account for him. Today, that account is worth $1,100. What was the annual rate of return on this account?

$1,100 = $100 (1+r)^44 r = ($1,100/$100)^(1/44) - 1 r = 0.0560 or 5.6%

If you earn an annual interest rate of 9.9%, how may years will it take to quadruple your money?

$4 = $1 (1.099)^t t = 14.69

You just purchase two coins at a price of $670 each. Because one of the coins is more collectible, you believe that its value will increase at a rate of 7.1% per year, while you believe the second coin will only increase at 6.5% per year. If you are correct, how much more will the first coin be worth in 15 years?

FV = $670 x 1.071^15 = $1,874.64 FV = $670 x 1.065^15 = $1,723.13 Difference = $1,874.64 - $1,723.13 = $151.50

Today, you dream car costs $68,800. You feel that the price of the car will increase at an annual rate 2.7%. If you plan to wait 7 years to buy the car, how much will it cost at that time?

FV = $68,800 x 1.027^7 = $82.905.16

The most recent census for a city indicated that there were 961,272 residents. The population of the city is expected to increase at an annual rate of 4.1% each year for the next 7 years. What will the population be at that time?

FV = 961,272 x 1.041^7 = 1,273,507

Thomas invests $114 in an account that pays 4% simple interest. How much money will Thomas have at the end of 6 years?

Balance Year 6 = $114 + ($114 x 0.04 x 6) = $141.36

Beatrice invests $1,350 in an account that pays 4% simple interest. How much more could she have earned over a 5-year period if the interest had been compounded annually?

Balance year 5 with simple interest = $1,350 + ($1,350 x 0.040 x 5) = $1,620 Balance year 5 with compound interest = $1,350 x 1.04^5 = $1,642.48 Additional interest = $1,642.48 - $1,620 = $22.48

You have $7,500 and will invest the money at an interest rate of 0.46% per month until the account is worth $13,00. How many years do you have to wait until you reach your target account value?

$13,000 = $7,500(1.0026)^t t = 211.83 months years to wait = 211.83/12 = 17.65 years

What is the future value of $3,098 invested in 9 years at 6.2% compounded annually?

FV = $3,098 x 1.062^9 = $5,323.56

One year ago, you invested $3,400. Today it is worth $4,150. What rate of interest did you earn?

FV = $4,150 = $3,400 x (1+r)^1 r = 0.2206 or 22.06%

What is the present value of $12,900 to be received 2 years from today if the discount rate is 6%?

PV = $12,900/1.06^2 = $11,480.95

You need to have $20,000 for a down payment on a house in 6 years. If you can earn an annual interest rate of 4.6%, how much will you have to deposit today?

PV = $20,000/1.046^6 = $15,270.03

Your bank will pay you an interest rate of 0.132% per week. You want to have $25,500 in 7 years. How much will you have to deposit today? Assume 52 weeks per year

PV = $25,500/1.00132^(7x52) = $15,776.40

You want to have $87,000 in 16 years to help your child attend college. If you can earn an annual interest rate of 4.3% how much will you have to deposit today?

PV = $87,000/1.043^16 = $44,357.83

You can invest in an account that pays simple interest or an account that pays compound interest. In either case, you plan to invest $3,900 today and both accounts have an annual interest rate of 5%. How much more interest will you receive in the 11th year in the account that pays compound interest?

Simple interest: Interest per year = $3,900 x 0.05 = $195 Compound interest: Value after 10 years = $4,900 x 1.05^10 = $6,352.69 Interest in year 11 = $6,352.69 x 0.05 = $317.63 Difference = $317.63 - $195 = $122.63