Question 1

Your coin collection contains fifty-four 1941 silver dollars.Your grandparents purchased them for their face value when they were new.These coins have appreciated at a 10 percent annual rate.How much will your collection be worth when you retire in 2060?

Accepted Answer

FV = $54 × (1.10)¹¹⁹ = $4,551,172

Question 2

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 × (1 + .045)^t; t = 21 years; Age today = 9 + 21 = 30

Question 3

Sixteen years ago,Alicia invested $500.Eight years ago,Travis invested $900.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 = $500 × (1 + r)¹⁶; r = 10.30 percentTravis: $2,400 = $900 × (1 + r)⁸; r = 13.04 percent Since both Alicia and Travis have equal account values today and since Travis earns the higher rate of return, his account had to be worth less than Alicia's account one year ago.

Question 4

Suppose that the first comic book of a classic series was sold in 1954.In 2000,the estimated price for this comic book in good condition was about $340,000.This represented a return of 27 percent per year.For this to be true,what was the original price of the comic book in 1954?

Accepted Answer

PV = $340,000 × [1/(1 + .27)⁴⁶; PV = $5.71

Question 5

In 1895,the winner of a competition was paid $150.In 2006,the winner's prize was $70,000.What will the winner's prize be in 2040 if the prize continues increasing at the same rate?

Accepted Answer

$70,000 = $150 × (1 = r)¹¹¹; r = 5.6927277 percentFV = $70,000 × (1 + .056927277)³⁴ = $459,866

Question 6

At 8 percent interest,how long would it take to quadruple your money?

Accepted Answer

$4 = $1 × (1 + .08)^t; t = 18.01 years

Question 7

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?

Accepted Answer

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

Question 8

You're trying to save to buy a new $160,000 Ferrari.You have $58,000 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 = $58,000 × (1 + .06)^t; t = 17.41 years

Question 9

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 × (1 + r)¹; r = 6.92 percent

Question 10

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 × (1 + r)⁴⁰; r = 11.78 percent

Question 11

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 × (1 + r)²; r = 8.78 percent

Question 12

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 × [1/(1.065)²⁵] = $176,067,311

Question 13

Theo needs $40,000 as a down payment for a house 6 years from now.He earns 2.5 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 × [1/(1 + .025)⁶] = $34,491.87Present value = $26,000 × [1/(1 + .025)⁵] = $35,354.17Difference = $35,354.17 - $34,491.87 = $862.30

Question 14

You have just received notification that you have won the $1.4 million first prize in the Centennial Lottery.However,the prize will be awarded on your 100^th birthday,78 years from now.The appropriate discount rate is 8 percent.What is the present value of your winnings?

Accepted Answer

PV = $1,400,000 × [1/(1.08)⁷⁸] = $3,459.99

Question 15

Suppose you are committed to owning a $140,000 Ferrari.You believe your mutual fund can achieve an annual rate of return of 8 percent and you want to buy the car in 7 years.How much must you invest today to fund this purchase assuming the price of the car remains constant?

Accepted Answer

PV = $140,000 × [1/(1 + .08)⁷; PV = $81,688.66

Question 16

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 17

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 × (1 + r)⁹; r = 4.20 percent

Question 18

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 × (1 + r)¹⁴; r = 9.34 percent

Question 19

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

Accepted Answer

Rule of 72 = 72/5 years = 14.4 percent interest

Question 20

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 6 percent per year?

Accepted Answer

$214,800 = $36,900 × (1 + .06)^t; t = 30.23 years

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