Finance 326 Chap 4

You have $5,000 you want to invest for the next 45 years. You are offered an investment plan that will pay you 6 percent per year for the next 15 years and 10 percent per year for the last 30 years. How much will you have at the end of the 45 years? How much will you have if the investment plan pays you 10 percent per year for the first 15 years and 6 percent per year for the next 30 years?

C. $209,092.54; $119,959.94 Future value A = $5,000 × (1 + 0.06)15 × (1 + 0.10)^30 = $209,092.54 Future value B = $5,000 × (1 + 0.10)15 × (1 + 0.06)^30 = $119,959.94

Ben invested $5,000 twenty years ago with an insurance company that has paid him 5 percent simple interest on his funds. Charles invested $5,000 twenty years ago in a fund that has paid him 5 percent interest, compounded annually. How much more interest has Charles earned than Ben over the past 20 years?

C. $3,266.49 Interest on interest = $5,000 × (1 + 0.05)^20 - [$5,000 + ($5,000 × 0.05 × 20)] = $3,266.49

Today, you deposit $2,400 in a bank account that pays 4 percent simple interest. How much interest will you earn over the next 5 years?

C. $480.00 Interest = $2,400 × 0.04 × 5 = $480

Assume the total cost of a college education will be $285,000 when your child enters college in 22 years. You presently have $35,000 to invest. What annual rate of interest must you earn on your investment to cover the cost of your child's college education?

C. 10.00 percent $285,000 = $35,000 × (1 + r)^22; r = 10.00 percent

Your friend claims that he invested $5,000 seven years ago and that this investment is worth $38,700 today. For this to be true, what annual rate of return did he have to earn? Assume the interest compounds annually.

C. 33.96 percent $38,700 = $5,000 × (1 + r)^7; r = 33.96 percent

Which of the following will increase the future value of a lump sum investment? I. Decreasing the interest rate II. Increasing the interest rate III. Increasing the time period IV. Decreasing the amount of the lump sum investment

C. II and III only

The interest rate used to compute the present value of a future cash flow is called the:

C. discount rate.

By definition, a bank that pays simple interest on a savings account will pay interest:

C. only on the principal amount originally invested.

Which one of the following is the correct formula for computing the present value of $600 to be received in 6 years? The discount rate is 7 percent.

D. PV = $600/(1 + 0.07)6

Jamie earned $180 in interest on her savings account last year. She has decided to leave the $180 in her account so that she can earn interest on the $180 this year. The interest Jamie earns this year on this $180 is referred to as:

D. interest on interest.

You are scheduled to receive $7,500 in three years. When you receive it, you will invest it for eight more years at 7.5 percent per year. How much will you have in eleven years?

A. $13,376.08 Future value = $7,500 × (1 + 0.075)^8 = $13,376.08

You want to have $25,000 for a down payment on a house 6 years from now. If you can earn 6.5 percent, compounded annually, on your savings, how much do you need to deposit today to reach your goal?

A. $17,133.35 Present value = $25,000/(1 + 0.065)^6 = $17,133.35

Ten years from now, you will be inheriting $100,000. What is this inheritance worth to you today if you can earn 5.5 percent interest, compounded annually?

A. $58,543.06 Present value = $100,000/(1 + 0.055)^10 = $58,543.06

You have been told that you need $25,600 today in order to have $100,000 when you retire 35 years from now. What rate of interest was used in the present value computation? Assume interest is compounded annually.

A. 3.97 percent $100,000 = $25,600 × (1 + r)^35; r = 3.97 percent

Suppose that in 2010, a $10 silver certificate from 1898 sold for $11,200. For this to have been true, what would the annual increase in the value of the certificate have been?

A. 6.47 percent $11,200 = $10 × (1 + r)^(2010 - 1898); r = 6.47 percent

Jenny needs to borrow $16,000 for 3 years. The loan will be repaid in one lump sum at the end of the loan term. Which one of the following interest rates is best for Jenny?

A. 8 percent simple interest

Sue needs to invest $3,626 today in order for her savings account to be worth $5,000 six years from now. Which one of the following terms refers to the $3,626?

A. Present value

The present value of a lump sum future amount:

A. increases as the interest rate decreases.

Given an interest rate of zero percent, the future value of a lump sum invested today will always:

A. remain constant, regardless of the investment time period.

Today, Stacy is investing $26,000 at 6.0 percent, compounded annually, for 4 years. How much additional income could he earn if he had invested this amount at 7 percent, compounded annually?

B. $1,256.30 Future value 6.0% = $26,000 × (1 + 0.060)^4 = $32,824.40 Future value 7% = $26,000 × (1 + 0.07)^4 = $34,080.70 Difference = $34,080.70 - $32,824.40 = $1,256.30

Travis invests $10,000 today into a retirement account. He expects to earn 8 percent, compounded annually, on his money for the next 26 years. After that, he wants to be more conservative, so only expects to earn 5 percent, compounded annually. How much money will he have in his account when he retires 38 years from now, assuming this is the only deposit he makes into the account?

B. $132,827.88 Future value = $10,000 × (1 + 0.08)^26 × (1 + 0.05)^(38 - 26) = $132,827.88

Your parents spent $6,200 to buy 500 shares of stock in a new company 13 years ago. The stock has appreciated 9 percent per year on average. What is the current value of those 500 shares?

B. $19,007.99 Future value = $6,200 × (1 + 0.09)^13 = $19,007.99

Precision Engineering invested $110,000 at 6.5 percent interest, compounded annually for 4 years. How much interest on interest did the company earn over this period of time?

B. $2,911.30 Interest on interest = $110,000 × (1 + 0.065)^4 - [$110,000 + ($110,000 × 0.065 × 4)] = $2,911.30

Jim just deposited $13,000 into his account at Traditions Bank. The bank will pay 1.3 percent interest, compounded annually, on this account. How much interest on interest will he earn over the next 15 years?

B. $244.20 Interest on interest = $13,000 × (1 + 0.013)^15 - [$13,000 + ($13,000 × 0.013 × 15)] = $244.20

You and your sister are planning a large anniversary party 3 years from today for your parents' 50th wedding anniversary. You have estimated that you will need $4,500 for this party. You can earn 2.5 percent compounded annually on your savings. How much would you and your sister have to deposit today in one lump sum to pay for the entire party?

B. $4,178.70 Present value = $4,500/(1 + 0.025)^3 = $4,178.70

Planters Bank pays 5 percent simple interest on its savings account balances, whereas Centura Bank pays 5 percent compounded annually. If you made a $12,000 deposit in each bank, how much more money would you earn from your Centura Bank account at the end of 20 years?

B. $7,839.57 Future value Planters = $12,000 + ($12,000 × 0.05 × 20) = $24,000 Future value Centura Street = $12,000 × (1 + 0.05)^20 = $31,839.57 Difference = $31,839.57 - $24,000 = $7,839.57

What is the future value of $4,900 invested for 8 years at 7 percent compounded annually?

B. $8,419.11 Future value = $4,900 × (1.07)^8 = $8,419.11

At 10 percent interest, how long does it take to quadruple your money?

B. 14.55 years $4 = $1 × (1 + 0.10)^t; t = 14.55 years

Terry invested $2,000 today in an investment that pays 6.5 percent annual interest. Which one of the following statements is correct, assuming all interest is reinvested?

B. Terry could have the same future value and invest less than $2,000 initially if he could earn more than 6.5 percent interest.

Tom earned $120 in interest on his savings account last year. Tom has decided to leave the $120 in his account so that he can earn interest on the $120 this year. This process of earning interest on prior interest earnings is called:

B. compounding.

Todd will be receiving a $10,000 bonus one year from now. The process of determining how much that bonus is worth today is called:

B. discounting.

Eric has $4,800 that he wants to invest for 4 years. He can invest this amount at his credit union and earn 4 percent simple interest. Or, he can open an account at Compass Bank and earn 3.65 percent interest, compounded annually. If he decides to invest at Copmpass Bank for 3 years, he will:

B. earn $27.89 less than if he had invested with his credit union. Credit union future value = $4,800 + ($4,800 × 0.04 × 4) = $5,568 Compass Bank future value = $4,800 × (1 + 0.0365)^4 = $5,540.11 Difference = $5,568 - $5,540.11 = $27.89

Martha is investing $5 today at 6 percent interest so she can have $10 later. The $10 is referred to as the:

B. future value.

The relationship between the present value and the time period is best described as:

B. inverse.

Skyline Industries will need $1.8 million 5 years from now to replace some equipment. Currently, the firm has some extra cash and would like to establish a savings account for this purpose. The account pays 5.25 percent interest, compounded annually. How much money must the company deposit today to fully fund the equipment purchase?

D. $1,393,676.52 Present value = $1,800,000/(1 + 0.0525)^5 = $1,393,676.52

Your coin collection contains ten 1939 silver dollars. If your great grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in 2050, assuming they appreciate at a 5.1 percent annual rate?

D. $2,499.78 Future value = $10 × (1 + 0.051)^(2050 - 1939) = $2,499.78

Your grandparents just gave you a gift of $15,000. You are investing this money for 12 years at 6 percent simple interest. How much money will you have at the end of the 12 years?

D. $25,800 Future value = $15,000 + ($15,000 × 0.06 × 12) = $25,800

You have just made your first $5,000 contribution to your individual retirement account. Assuming you earn a 5 percent rate of return and make no additional contributions, what will your account be worth when you retire in 35 years? What if you wait for 5 years before contributing?

D. $27,580.08; 21,609.71 Future value 35 years = $5,000 × (1 + 0.05)^35 = $27,580.08 Future value 30 years = $5,000 × (1 + 0.05)^30 = $21,609.71

You want to have $45,000 in cash to buy a car 4 years from today. You expect to earn 4.5 percent, compounded annually, on your savings. How much do you need to deposit today if this is the only money you save for this purpose?

D. $37,735.26 Present value = $45,000/(1 + 0.045)^4 = $37,735.26

You want to invest an amount of money today and receive back twice that amount in the future. You expect to earn 6 percent interest. Approximately how long must you wait for your investment to double in value?

D. 12 years Approximate time period = 72/6 = 12 years

You have $1,100 today and want to triple your money in 5 years. What interest rate must you earn if the interest is compounded annually?

D. 24.57 percent $3,300 = $1,100 × (1 + r)^5; r = 24.57 percent

Lisa has $1,000 in cash today. Which one of the following investment options is most apt to double her money?

D. 8 percent interest for 9 years

How long will it take to double your savings if you earn 7.2 percent interest, compounded annually?

D. 9.97 years $2 = $1 × (1 + 0.072)^t; t = 9.97 years

Which one of the following will increase the present value of a lump sum future amount? Assume the interest rate is a positive value and all interest is reinvested.

D. Decrease in the interest rate

Which one of the following is the correct formula for the future value of $500 invested today at 7 percent interest for 8 years?

D. FV = $500 (1 + 0.07)8

Jeff deposits $3,000 into an account which pays 2.5 percent interest, compounded annually. At the same time, Kurt deposits $3,000 into an account paying 5 percent interest, compounded annually. At the end of three years:

D. Kurt will have a larger account value than Jeff will.

Angela has just received an insurance settlement of $35,000. She wants to save this money until her daughter goes to college. If she can earn an average of 5.5 percent, compounded annually, how much will she have saved when her daughter enters college 10 years from now?

E. $59,785.06 Future value = $35,000 × (1 + 0.055)^10 = $59,785.06

Twelve years ago, you deposited $3,400 into an account. Seven years ago, you added an additional $1,000 to this account. You earned 8 percent, compounded annually, for the first 5 years and 5.5 percent, compounded annually, for the last 7 years. How much money do you have in your account today?

E. $8,721.97 Future value = {[$3,400 × (1 + 0.08)^5] + $1,000} × (1 + 0.055)^7 = $8,721.97

You just won $50,000 and deposited your winnings into an account that pays 5.5 percent interest, compounded annually. How long will you have to wait until your winnings are worth $100,000?

E. 12.95 years $100,000 = $50,000 × (1 + 0.055)^t; t = 12.95 years

Isaac only has $690 today but needs $800 to buy a new laptop. How long will he have to wait to buy the laptop if he earns 5.4 percent compounded annually on his savings?

E. 2.81 years $800 = $690 × (1 + 0.054)^t; t = 2.81 years

You expect to receive $20,000 at graduation one year from now. You plan on investing it at 6 percent until you have $100,000. How long will you wait from now?

E. 28.62 years $100,000 = $20,000 × (1 + 0.06)^t; t = 27.62 years Wait time = 1 + 27.62 = 28.62 years

You're trying to save to buy a new $210,000 Ferrari. You have $38,000 today that can be invested at your bank. The bank pays 4.1 percent annual interest on its accounts. How long will it be before you have enough to buy the car?

E. 42.54 years $210,000 = $38,000 × (1 + 0.041)^t; t = 42.54 years

Sam wants to invest $5,000 for 5 years. Which one of the following rates will provide him with the largest future value?

E. 7 percent interest, compounded annually

You have $1,500 today in your savings account. How long must you wait for your savings to be worth $4,000 if you are earning 1.1 percent interest, compounded annually?

E. 89.66 years $4,000 = $1,500 × (1 + 0.011)^t; t = 89.66years

When you were born, your parents opened an investment account in your name and deposited $500 into the account. The account has earned an average annual rate of return of 4.8 percent. Today, the account is valued at $36,911.22. How old are you?

E. 91.75 years $36,911.22 = $500 × (1 + 0.048)^t; t = 91.75 years

Which of the following will decrease the future value of a lump sum investment made today assuming that all interest is reinvested? Assume the interest rate is a positive value. I. Increase in the interest rate II. Decrease in the lump sum amount III. Increase in the investment time period IV. Decrease in the investment time period

E. II and IV only

Sara is investing $1,000 today. Which one of the following will increase the future value of that amount?

E. Increasing the interest rate.

Sixty years ago, your grandparents opened two savings accounts and deposited $200 in each account. The first account was with City Bank at 3 percent, compounded annually. The second account was with Country Bank at 3.5 percent, compounded annually. Which one of the following statements is true concerning these accounts?

E. The Country Bank account has paid $397.30 more in interest than the City Bank account. Future value City Bank = $200 × (1 + 0.03)^60 = $1,178.32 Future value Country Bank = $200 × (1 + 0.035)^60 = $1,575.62 Difference = $1,575.62 - $1,178.32 = $397.30

Which one of the following is a correct statement, all else held constant?

E. The future value is directly related to the interest rate.

Today, Courtney wants to invest less than $5,000 with the goal of receiving $5,000 back some time in the future. Which one of the following statements is correct?

E. The period of time she has to wait decreases as the amount she invests today increases.

Lester had $6,270 in his savings account at the beginning of this year. This amount includes both the $6,000 he originally invested at the beginning of last year plus the $270 he earned in interest last year. This year, Lester earned a total of $282.15 in interest even though the interest rate on the account remained constant. This $282.15 is best described as:

E. compound interest.

Computing the present value of a future cash flow to determine what that cash flow is worth today is called:

E. discounted cash flow valuation.

Centre Bank pays 2.5 percent interest, compounded annually, on its savings accounts. Country Bank pays 2.5 percent simple interest on its savings accounts. You want to deposit sufficient funds today so that you will have $1,500 in your account 2 years from today. The amount you must deposit today:

E. will be greater if you invest with Country Bank.