intro to finance chapter 5 questions

Phillippe invested $1,000 ten years ago and expected to have $1,800 today. He has not added or withdrawn any money from this account since his initial investment. All interest was reinvested in the account. As it turns out, he only has $1,680 in his account today. Which one of the following must be true?

He earned a lower interest rate than he expected.

What is the present value of $42,000 to be received 22 years from today if the discount rate is 14 percent?

Present value = $42,000/(1 + .14)^22 = $2,351.49

Your father invested a lump sum 33 years ago at 4.25 percent interest. Today, he gave you the proceeds of that investment which totaled $51,480.79. How much did your father originally invest?

Present value = $51,480.79/(1 + .0425)^33 = $13,035.72

You would like to give your daughter $75,000 towards her college education 17 years from now. How much money must you set aside today for this purpose if you can earn 8 percent on your investments?

Present value = $75,000/(1 + .08)^17 = $20,270.17

Kurt won a lottery and will receive $1,000 a year for the next 50 years. The value of his winnings today discounted at his discount rate is called which one of the following?

Present value.

You're trying to save to buy a new $72,000 sports car You have $38,000 today that can be invested at your bank. The bank pays 1.26 percent annual interest on its accounts. How many years will it be before you have enough to buy the car assuming the price of the car remains constant?

$72,000 = $38,000 ×(1 + .0126)t; t = 51.04 years

You hope to buy your dream car four years from now. Today, that car costs $54,500. You expect the price to increase by an average of 3.1 percent per year over the next four years. How much will your dream car cost by the time you are ready to buy it?

Future value = $54,500 ×(1 + .031)^4 = $61,578.79

You own a classic car that is currently valued at $64,000. If the value increases by 2.5 percent annually, how much will the car be worth 15 years from now?

Future value = $64,000 ×(1 + .025)^15 = $92,691.08

You are investing $100 today in a savings account at your local bank. Which one of the following terms refers to the value of this investment one year from now?

Future value.

One year ago, you invested $1,800. Today it is worth $1,924.62. What rate of interest did you earn?

$1,924.62 = $1,800 ×(1 + r)^1; r = 6.92 percent

Twelve years ago, your parents set aside $8,000 to help fund your college education. Today, that fund is valued at $23,902. What rate of interest is being earned on this account?

$23,902 = $8,000 ×(1 + r)12; r = 9.55 percent

Towne Station is saving money to build a new loading platform. Three years ago, they set aside $23,000 for this purpose. Today, that account is worth $31,406. What rate of interest is Towne Station earning on this investment?

$31,406 = $23,000 ×(1 + r)^3; r = 10.94 percent

Ten years ago, Jackson Supply set aside $130,000 in case of a financial emergency. Today, that account has increased in value to $330,592. What rate of interest is the firm earning on this money?

$330,592 = $130,000 ×(1 + r)^10; r = 9.78 percent

Assume the average vehicle selling price in the United States last year was $35,996. The average price 4 years earlier was $29,208. What was the annual increase in the selling price over this time period?

$35,996 = $29,208 ×(1 + r)4; r = 5.36 percent

At 6 percent interest, how long would it take to quadruple your money?

$4 = $1 ×(1 + .06)t; t = 23.79 years

Christina invested $3,000 five years ago and earns 2 percent interest on her investment. By leaving her interest earnings in her account, she increases the amount of interest she earns each year. The way she is handling her interest income is referred to as which one of the following?

Compounding.

Andy deposited $3,000 this morning into an account that pays 5 percent interest, compounded annually. Barb also deposited $3,000 this morning into an account that pays 5 percent interest, compounded annually. Andy will withdraw his interest earnings and spend it as soon as possible. Barb will reinvest her interest earnings into her account. Given this, which one of the following statements is true?

Barb will earn more interest the second year than Andy.

Today, you earn a salary of $28,000. What will be your annual salary twelve years from now if you earn annual raises of 2.6 percent?

Future value = $28,000 ×(1 + .026)^12 = $38,100.12

Interest earned on both the initial principal and the interest reinvested from prior periods is called:

Compound interest.

Steve just computed the present value of a $10,000 bonus he will receive in the future. The interest rate he used in this process is referred to as which one of the following?

Discount rate.

The process of determining the present value of future cash flows in order to know their worth today is referred to as:

Discounted cash flow valuation.

Terry is calculating the present value of a bonus he will receive next year. The process he is using is called:

Discounting

Al invested $7,200 in an account that pays 4 percent simple interest. How much money will he have at the end of five years?

Ending value = $7,200 + ($7,200 ×.04 ×5) = $8,640

What is the future value of $11,600 invested for 17 years at 7.25 percent compounded annually?

Future value = $11,600 ×(1 + .0725^)17 = $38,125.20

Your grandmother has promised to give you $10,000 when you graduate from college. She is expecting you to graduate three years from now. What happens to the present value of this gift if you speed up your graduation by one year and graduate two years from now?

Increases

Art invested $100 two years ago at 8 percent interest. The first year, he earned $8 interest on his $100 investment. He reinvested the $8. The second year, he earned $8.64 interest on his $108 investment. The extra $.64 he earned in interest the second year is referred to as:

Interest on interest.

Which one of the following variables is the exponent in the present value formula?

Number of time periods

Imprudential, Inc. has an unfunded pension liability of $627 million that must be paid in 21 years. To assess the value of the firm's stock, financial analysts want to discount this liability back to the present. The relevant discount rate is 7.38 percent. What is the present value of this liability?

PV = $627,000,000/(1.0738)21 = $140,564,661

Sue and Neal are twins. Sue invests $5,000 at 7 percent when she is 25 years old. Neal invests $5,000 at 7 percent when he is 30 years old. Both investments compound interest annually. Both Sue and Neal retire at age 60. Which one of the following statements is correct assuming neither Sue nor Neal withdraw any money from their accounts prior to retiring?

Sue will have more money than Neal at age 60.

What is the relationship between present value and future value interest factors?

The factors are reciprocals of each other.