Question 1

You are considering two lottery payment options:
 Option A pays $10,000 today and Option B pays $20,000 at the end of ten years. Assume you can earn 6 percent on your savings. Which option will you choose if you base your decision on present values?
 Which option will you choose if you base your decision on future values?
 Explain why your answers are either the same or different.

Accepted Answer

The answer of You are considering two lottery payment options:
...

Question 2

Assume the total cost of a college education will be $300,000 when your child enters college in 16 years. You presently have $75,561 to invest. What rate of interest must you earn on your investment to cover the cost of your child's college education?

Accepted Answer

$300,000 = $75,561 (1 + r)¹⁶; r = 9 percent

Question 3

Fifteen 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?

Accepted Answer

$330,592 = $130,000 F1F1F1S1F1F1F10 (1 + r)¹⁵; r = 6.42 percent

Question 4

Theo needs $40,000 as a down payment for a house 6 years from now. He earns 3.5 percent on his savings. Theo can either deposit one lump sum today for this purpose or he can wait a year and deposit a lump sum. How much additional money must he deposit if he waits for one year rather than making the deposit today?

Accepted Answer

Present value = $40,000 F1F1F1S1F1F1F10 [1/(1 + .035)⁶] = $32,540.03Present value = $26,000 F1F1F1S1F1F1F10 [1/(1 + .035)⁵] = $33,678.93Difference = $33,678.93 - $32,540.03 = $1,138.90

Question 5

You're trying to save to buy a new $160,000 Ferrari. You have $56,000 today that can be invested at your bank. The bank pays 6 percent annual interest on its accounts. How many years will it be before you have enough to buy the car? Assume the price of the car remains constant.

Accepted Answer

$160,000 = $56,000 F1F1F1S1F1F1F10 (1 + .06)^t; t = 18.02 years

Question 6

On your ninth birthday, you received $300 which you invested at 4.5 percent interest, compounded annually. Your investment is now worth $756. How old are you today?

Accepted Answer

$756 = $300 F1F1F1S1F1F1F10 (1 + .045)^t; t = 21 years; Age today = 9 + 21 = 30

Question 7

Sixteen years ago, Alicia invested $1,000. Eight years ago, Travis invested $2,000. Today, both Alicia's and Travis' investments are each worth $2,400. Assume that both Alicia and Travis continue to earn their respective rates of return. Which one of the following statements is correct concerning these investments?

Accepted Answer

Alicia: $2,400 = $1,000 F1F1F1S1F1F1F10 (1 + r)¹⁶; r = 5.62 percentTravis: $2,400 = $2,000 F1F1F1S1F1F1F10 (1 + r)⁸; r = 2.31 percent Since both Alicia and Travis have equal account values today and since Alicia earns the higher rate of return, her account had to be worth less than Travis' account one year ago.

Question 8

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

Accepted Answer

$1,924.62 = $1,800 F1F1F1S1F1F1F10 (1 + r)¹; r = 6.92 percent

Question 9

Fourteen years ago, your parents set aside $7,500 to help fund your college education. Today, that fund is valued at $26,180. What rate of interest is being earned on this account?

Accepted Answer

$26,180 = $7,500 F1F1F1S1F1F1F10 (1 + r)¹⁴; r = 9.34 percent

Question 10

At 11 percent interest, how long would it take to quadruple your money?

Accepted Answer

$4 = $1 F1F1F1S1F1F1F10 (1 + .11)^t; t = 13.28 years

Question 11

Some time ago, Julie purchased eleven acres of land costing $36,900. Today, that land is valued at $214,800. How long has she owned this land if the price of the land has been increasing at 10.5 percent per year?

Accepted Answer

$214,800 = $36,900 F1F1F1S1F1F1F10 (1 + .105)^t; t = 17.64 years

Question 12

You are considering two separate investments. Both investments pay 7 percent interest. Investment A pays simple interest and Investment B pays compound interest. Which investment should you choose, and why, if you plan on investing for a period of 5 years?

Accepted Answer

The answer of You are considering two separate investments. Both...

Question 13

According to the Rule of 72, you can do which one of the following?

Accepted Answer

Rule of 72 = 72/8 years = 9 percent interest

Question 14

You want to deposit sufficient money today into a savings account so that you will have $1,000 in the account three years from today. Explain why you could deposit less money today if you could earn 3.5 percent interest rather than 3 percent interest.

Accepted Answer

The answer of You want to deposit sufficient money today...

Question 15

Forty years ago, your mother invested $5,000. Today, that investment is worth $430,065.11. What is the average annual rate of return she earned on this investment?

Accepted Answer

$430,065.11 = $5,000 F1F1F1S1F1F1F10 (1 + r)⁴⁰; r = 11.78 percent

Question 16

What lesson does the future value formula provide for young workers who are looking ahead to retiring some day?

Accepted Answer

The answer of What lesson does the future value formula...

Question 17

Penn Station is saving money to build a new loading platform. Two years ago, they set aside $24,000 for this purpose. Today, that account is worth $28,399. What rate of interest is Penn Station earning on this investment?

Accepted Answer

$28,399 = $24,000 F1F1F1S1F1F1F10 (1 + r)²; r = 8.78 percent

Question 18

Assume the average vehicle selling price in the United States last year was $41,996. The average price 9 years earlier was $29,000. What was the annual increase in the selling price over this time period?

Accepted Answer

$41,996 = $29,000 F1F1F1S1F1F1F10 (1 + r)⁹; r = 4.20 percent

Question 19

At an interest rate of 10 percent and using the Rule of 72, how long will it take to double the value of a lump sum invested today?
 How long will it take after that until the account grows to four times the initial investment?
 Given the power of compounding, shouldn't it take less time for the money to double the second time?

Accepted Answer

The answer of At an interest rate of 10 percent...

Question 20

Imprudential, Inc. has an unfunded pension liability of $850 million that must be paid in 25 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 6.5 percent. What is the present value of this liability?

Accepted Answer

PV = $850,000,000 F1F1F1S1F1F1F10 [1/(1.065)²⁵] = $176,067,311

Quiz 5: Introduction to Valuation: The Time Value of Money