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- Georgia
- Georgia Institute of Technology
- Finance Chapter 5

Hannah B.

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

future value

Tracy invested $1,000 fiveyears ago and earns 4 percent interest on her investment. By leaving herinterest earnings in her account, she increases the amount of interest sheearns each year. The way she is handling her interest income is referred to aswhich one of the following?

compounding

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Steve invested $100 twoyears ago at 10 percent interest. The first year, he earned $10 interest on his$100 investment. He reinvested the $10. The second year, he earned $11 intereston his $110 investment. The extra $1 he earned in interest the second year isreferred to as:

interest on interest

Interest earned on both theinitial principal and the interest reinvested from prior periods iscalled:

compound interest

Sara invested $500 sixyears ago at 5 percent interest. She spends her earnings as soon as she earnsany interest so she only receives interest on her initial $500 investment.Which type of interest is Sara earning?

simple interest

Shelley won a lottery andwill receive $1,000 a year for the next ten years. The value of her winningstoday discounted at her discount rate is called which one of thefollowing?

present value

Terry is calculating thepresent value of a bonus he will receive next year. The process he is using iscalled:

discounting

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

discount rate

discounted cash flow valuation

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

Barb will earn interest on interest

Sue and Neal are twins. Sueinvests $5,000 at 7 percent when she is 25 years old. Neal invests $5,000 at 7percent 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 iscorrect assuming that neither Sue nor Neal has withdrawn any money from theiraccounts?

A. Sue will have less money when she retiresthan Neal.

A. Sue will have less money when she retiresthan Neal.

Sue will have more money than Neal as long as they retire at the same time

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Samantha opened a savingsaccount this morning. Her money will earn 5 percent interest, compoundedannually. After five years, her savings account will be worth $5,600. Assumeshe will not make any withdrawals. Given this, which one of the followingstatements is true?

Samantha could havedeposited less money and still had $5,600 in five years if she could have earned5.5 percent interest.

This afternoon, youdeposited $1,000 into a retirement savings account. The account will compoundinterest at 6 percent annually. You will not withdraw any principal or interestuntil you retire in forty years. Which one of the following statements iscorrect?

The present value of thisinvestment is equal to $1,000.

Your grandmother haspromised to give you $5,000 when you graduate from college. She is expectingyou to graduate two years from now. What happens to the present value of thisgift if you delay your graduation by one year and graduate three years fromnow?

decreases

Luis is going to receive$20,000 six years from now. Soo Lee is going to receive $20,000 nine years fromnow. Which one of the following statements is correct if both Luis and Soo Leeapply a 7 percent discount rate to these amounts?

In today's dollars, Luis' money is worth more than Soo Lee's

Which one of the followingvariables is the exponent in the present value formula?

time

You want to have $1 millionin your savings account when you retire. You plan on investing a single lumpsum today to fund this goal. You are planning on investing in an account whichwill pay 7.5 percent annual interest. Which of the following will reduce theamount that you must deposit today if you are to have your desired $1 millionon the day you retire?

I and III only

Which one of the followingwill produce the highest present value interest factor?

6 percent interest for five years

What is the relationshipbetween present value and future value interest factors?

The factors are reciprocals of each other

Martin invested $1,000 sixyears ago and expected to have $1,500 today. He has not added or withdrawn anymoney from this account since his initial investment. All interest wasreinvested in the account. As it turns out, Martin only has $1,420 in hisaccount today. Which one of the following must be true?

Martin earned a lower interest rate than he expected

Gerold invested $6,200 inan account that pays 5 percent simple interest. How much money will he have atthe end of ten years?

$9,300

Alex invested $10,500 in anaccount that pays 6 percent simple interest. How much money will he have at theend of four years?

$13,020

You invested $1,650 in anaccount that pays 5 percent simple interest. How much more could you haveearned over a 20-year period if the interest had compounded annually?

$1,077.94

Travis invested $9,250 inan account that pays 6 percent simple interest. How much more could he haveearned over a 7-year period if the interest had compounded annually?

$773.58

What is the future value of$7,189 invested for 23 years at 9.25 percent compounded annually?

$54,999.88

Today, you earn a salary of$36,000. What will be your annual salary twelve years from now if you earnannual raises of 3.6 percent?

$55,032.54

You own a classicautomobile that is currently valued at $147,900. If the value increases by 6.5percent annually, how much will the automobile be worth ten years fromnow?

$277,628.63

You hope to buy your dreamcar four years from now. Today, that car costs $82,500. You expect the price toincrease by an average of 4.8 percent per year over the next four years. Howmuch will your dream car cost by the time you are ready to buy it?

$99,517.41

This morning, TL Truckinginvested $80,000 to help fund a company expansion project planned for 4 yearsfrom now. How much additional money will the firm have 4 years from now if itcan earn 5 percent rather than 4 percent on its savings?

$3,651.82

You just received $225,000from an insurance settlement. You have decided to set this money aside andinvest it for your retirement. Currently, your goal is to retire 25 years fromtoday. How much more will you have in your account on the day you retire if youcan earn an average return of 10.5 percent rather than just 8 percent?

$1,189,576

You just received a $5,000gift from your grandmother. You have decided to save this money so that you cangift it to your grandchildren 50 years from now. How much additional money willyou have to gift to your grandchildren if you can earn an average of 8.5percent instead of just 8 percent on your savings?

$60,923.52

You are depositing $1,500in a retirement account today and expect to earn an average return of 7.5percent on this money. How much additional income will you earn if you leavethe money invested for 45 years instead of just 40 years?

$11,790.90

You collect old coins.Today, you have two coins each of which is valued at $250. One coin is expectedto increase in value by 6 percent annually while the other coin is expected toincrease in value by 4.5 percent annually. What will be the difference in thevalue of the two coins 15 years from now?

$115.32

Your father invested a lumpsum 26 years ago at 4.25 percent interest. Today, he gave you the proceeds ofthat investment which totaled $51,480.79. How much did your father originallyinvest?

$17,444.86

What is the present valueof $150,000 to be received 8 years from today if the discount rate is 11percent?

$65,088.97

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

$20,270.17

You want to have $35,000saved 6 years from now to buy a house. How much less do you have to deposittoday to reach this goal if you can earn 5.5 percent rather than 5 percent onyour savings? Today's deposit is the only deposit you will make to this savingsaccount.

$733.94

Your older sister deposited$5,000 today at 8.5 percent interest for 5 years. You would like to have justas much money at the end of the next 5 years as your sister will have. However,you can only earn 7 percent interest. How much more money must you deposittoday than your sister did if you are to have the same amount at the end of the5 years?

$360.43

A year ago, you deposited$30,000 into a retirement savings account at a fixed rate of 5.5 percent.Today, you could earn a fixed rate of 6.5 percent on a similar type account.However, your rate is fixed and cannot be adjusted. How much less could youhave deposited last year if you could have earned a fixed rate of 6.5 percentand still have the same amount as you currently will when you retire 38 yearsfrom today?

$9,234.97 less

When you retire 40 yearsfrom now, you want to have $1.2 million. You think you can earn an average of12 percent on your investments. To meet your goal, you are trying to decidewhether to deposit a lump sum today, or to wait and deposit a lump sum 2 yearsfrom today. How much more will you have to deposit as a lump sum if you waitfor 2 years before making the deposit?

$3,280.78

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

$1,138.90

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

6.92 percent

According to the Rule of72, you can do which one of the following?

double your money in 8 years at 9 percent interest

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

11.78 percent

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

One year ago, Alicia's investment was worth less than Travis' investment

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

8.78 percent

Fifteen years ago, JacksonSupply set aside $130,000 in case of a financial emergency. Today, that accounthas increased in value to $330,592. What rate of interest is the firm earningon this money?

6.42 percent

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

9.34 percent

Some time ago, Juliepurchased 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 beenincreasing at 10.5 percent per year?

17.64 years

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

age 30

When you can earn more interest, you need less of your own money to reach the same future dollar amount

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

Simple interest is interestearned on the initial principal amount only. Compound interest is interestearned on both the initial principal and all prior interest earnings that havebeen reinvested. You should choose Investment B which pays compound interest asyou will earn more interest income over the 5 years by doing so.

What lesson does the futurevalue formula provide for young workers who are looking ahead to retiring someday?

The future value formulais: FV = PV (1 + r)^{t}. Time is the exponent. While the rate of returnis important and has a direct affect on the growth of an investment account,time is critical. To maximize retirement income, workers need to commencesaving when they are young so that reinvested earnings have time to compound.

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

PV of A = $10,000; PV of B= $11,167.90; FV of A = $17,908.48; FV of B = $20,000. Based on both presentvalues and future values, B is the better choice. Students should explain thatcomputing present values and computing future values are simply inverse processesof one another, and that choosing between two lump sums based on present valueswill always give the same result as choosing between the same two lump sumsbased on future values.

At an interest rate of 10percent and using the Rule of 72, how long will it take to double the value ofa lump sum invested today? How long will it take after that until the accountgrows 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?

It will take 7.2 years todouble the initial investment, then another 7.2 years to double it again. Thatis, it takes 14.4 years for the value to reach four times the initialinvestment.

56. Assume the totalcost of a college education will be $300,000 when your child enters college in16 years. You presently have $75,561 to invest. What rate of interest must youearn on your investment to cover the cost of your child's collegeeducation?

9.00 percent

At 11 percent interest, howlong would it take to quadruple your money

13.28 years

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

4.20 percent

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

18.02 years

Imprudential, Inc. has anunfunded pension liability of $850 million that must be paid in 25 years. Toassess the value of the firm's stock, financial analysts want to discount thisliability back to the present. The relevant discount rate is 6.5 percent. Whatis the present value of this liability?

$176,067,311

You have just receivednotification that you have won the $1.4 million first prize in the CentennialLottery. However, the prize will be awarded on your 100^{th} birthday,70 years from now. The appropriate discount rate is 8 percent. What is thepresent value of your winnings?

$6,404.20

Your coin collectioncontains fifty-four 1941 silver dollars. Your grandparents purchased them fortheir face value when they were new. These coins have appreciated at a 10percent annual rate. How much will your collection be worth when you retire in2060?

$4,551,172

In 1895, the winner of acompetition was paid $110. In 2006, the winner's prize was $70,000. What willthe winner's prize be in 2040 if the prize continues increasing at the samerate?

$505,697

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

$5.71

Suppose you are committedto owning a $140,000 Ferrari. You believe your mutual fund can achieve anannual rate of return of 9 percent and you want to buy the car in 7 years. Howmuch must you invest today to fund this purchase assuming the price of the carremains constant?

$76,584.79

You have just made a $1,500contribution to your individual retirement account. Assume you earn a 12percent rate of return and make no additional contributions. How much more willyour account be worth when you retire in 25 years than it would be if youwaited another 10 years before making this contribution?

$17,289.75

You are scheduled toreceive $30,000 in two years. When you receive it, you will invest it for 5more years, at 8 percent per year. How much money will you have 7 years fromnow?

$44,079.84

You expect to receive$9,000 at graduation in 2 years. You plan on investing this money at 10 percentuntil you have $60,000. How many years will it be until this occurs?

$21.90 years

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