FIN5008 - ch. 4

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?

$2,499.78 10 (1 + 0.051) ^ 111 = 2,499.778 ~ $2,499.78 FV = PV (1 + r) ^ t

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?

$209,092.54; $119,959.94 FV = 5,000(1.06)^15 FV = 11982.7909(1.10)^30 FV = 209,092.5387 ~ 209,092.54 FV = 5,000(1.10)^15 FV = 20886.2408(1.06)^30 FV = 119,959.9399 ~ 119,959.94

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?

$244.20

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?

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

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?

$37,735.26 PV = 45,000 / (1.045)^4 PV = 37,735.26 PV = FV / (1+r)^t

If a savings account pays 6% p.a. interest rate, how much money do you need to deposit to accumulate $72,428 in 10 years? Note that the bank will compound interest monthly.

$39,808.80 PV = 72,428 / (1 + 0.06/12)^(12*10) PV = 72,428 / (1.005)^120 PV = 72,428 / 1.8193967 PV = 39,808.80 PV = FV / (1 + (r/12)) ^(t*12)

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?

$4,178.70 PV = 4,500 / (1+0.025)^3 PV = 4,500 / 1.076890625 PV = 7,178.6973 ~ 4,178.70 PV = FV / (1+r)^t

Which one of the following is the correct formula for the future value of $500 invested today at 7 percent interest for 8 years? - FV = $500 (1 + 0.08)7 - FV = $500/(0.07 × 8) - FV = $500/[(1 + 0.08) × 7] - FV = $500 (1 + 0.07)8 - FV = $500/[(1 + 0.07) × 8]

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: - Both Jeff and Kurt will have accounts of equal value. - Jeff will have more money saved than Kurt. - Kurt will earn exactly twice the amount of interest that Jeff earns. - Kurt will have a larger account value than Jeff will. - Kurt will have twice the money saved that Jeff does.

Kurt will have a larger account value than Jeff will.

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. - PV = $600 × (0.07 × 6) - PV = $600/(1 + 6)0.07 - PV = $600 (1 + 0.07)6 - PV = $600/(1 + 0.07)6 - PV = $600 (1 + 6)7

PV = $600/(1 + 0.07)^6

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? - Factor value - Compound value - Present value - Complex value - Future value

Present value

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?

$480.00 SIFV = (5)(2400)(0.04) SIFV = 480 (interest only) SIFV = PV + (t)(PV)(r)

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? - 7 years - 6 years - 14 years - 12 years - 8 years

12 years t = ln(2/1) / ln(1+0.06) t = 11.8956 ~ 12 t = [ln(FV/PV) / ln(1+r)]

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?

12.95 years t = ln(100,000/50,000) / ln(1 + 0.055) t = 12.94615 ~ 12.95 t = [ln(FV/PV) / ln(1+r)]

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?

13,376.08 FV = 7,500 (1+0.075)^8 FV = 7,500 (1.075)^8 FV = 13,376.08 FV = PV(1+r)^t

Currently you have $750,375 in your IRA account, and want to retire when its balance becomes $3 million. If you can earn 10% p.a. return, in how many years can you retire? (Note: Type in your answer with 2 digits after decimal point. For example, type in "15.83".)

14.54 t = [ln(3,000,000 / 750,375) / ln(1.10)] t = 14.539 ~ 14.54 t = [ln(FV/PV) / ln(1+r)]

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

14.55 years t = ln(4/1) / ln(1.10) t = 14.545 ~ 14.55 t = [ln(FV/PV) / ln(1+r)]

Currently you have $722,173 in your IRA account, and want to retire when its balance becomes $3 million. If you can earn 10% p.a. return, in how many years can you retire? (Note: Type in your answer with 2 digits after decimal point. For example, type in "15.83".)

14.94 years t = {[ln(3,000,000 / 772,173] / ln(1+0.10) t = 14.94177 ~ 14.94 t = [ln(FV/PV) / ln(1+r)]

Currently you have $602,404 in your IRA account, and want to retire when its balance becomes $3 million. If you can earn 10% p.a. return, in how many years can you retire? (Note: Type in your answer with 2 digits after decimal point. For example, type in "15.83".)

16.84 t = [ln(3,000,000 / 602,404) / ln(1.10)] t = 16.844 ~ 16.84 t = [ln(FV/PV) / ln(1+r)]

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?

2.81 years t = [ln(800/690) / ln(1.054)] t = 2.81257 ~ 2.81 t = [ln(FV/PV) / ln(1+r)]

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.

3.97% r = (100,000 / 25,600) ^(1/35) - 1 = 1.039698 - 1 = 0.039698 ~ 3.97% r = (FV / PV)^(1/t) - 1

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.

33.96% r = (38,700 / 5,000)^(1/7) - 1 r = (7.74) ^(0.142857) - 1 r = 1.33956 - 1 = 0.33956 ~ 33.96% r = (FV / PV)^(1/t) - 1

If a savings account pays 7% p.a. interest rate, how much money do you need to deposit to accumulate $79,018 in 10 years? Note that the bank will compound interest monthly.

39319.06 PV = 79,018 / (1 + (0.07/12))^(10*12) PV = 79,018 / 2.0096613767 PV = 39,319.0618659 ~ 39319.06 PV = FV / (1 + (r/12)) ^(t*12)

If a savings account pays 7% p.a. interest rate, how much money do you need to deposit to accumulate $75,030 in 9 years? Note that the bank will compound interest monthly.

40,033.57 PV = 75,030 / (1 + 0.07/12)^(9*12) PV = 75,030 / 1.8741769 PV = 40,033.5742 ~ 40,033.75 PV = FV / (1 + r/12)^(t*12)

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? - 8.5 percent interest, compounded annually - 8 percent interest, compounded annually - 9 percent interest, compounded annually - 8.5 percent simple interest - 8 percent simple interest

8 percent simple interest

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?

89.66 years t = [ln(4,000 / 1,500) / ln(1.011)] t = 89.6558 ~ 89.66 t = [ln(FV/PV) / ln(1+r)]

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

9.97 years [ln(2/1) / ln(1+0.72) = 0.693127 / 0.0695260 = 9.969 ~ 9.97 t = [ln(FV/PV) / ln(1+r)]

The present value of a lump sum future amount: - is inversely related to the future value. - is directly related to the time period. - decreases as the time period decreases. - increases as the interest rate decreases. - is directly related to the interest rate.

increases as the interest rate decreases.

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:

interest on interest

The relationship between the present value and the time period is best described as: - direct. - parallel. - ambiguous. - unrelated. - inverse.

inverse.

By definition, a bank that pays simple interest on a savings account will pay interest: - only at the beginning of the investment period. - on both the principal amount and the reinvested interest. - only if all previous interest payments are reinvested. - only on the principal amount originally invested. - on interest.

only on the principal amount originally invested.

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?

$17,133.35 PV = (25,000 / (1.065)^6 PV = 25,000 / 1.45914229654 PV = 17,133.3529 ~ 17,133.35 PV = FV / (1+r)^t

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?

$59,785.06 FV = 35,000(1+0.055)^10 FV = 35,000(1.70814445835) FV = 59,785.056 ~ 59,785.06 FV = PV(1+r)^t

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?

$7,839.57 Planters Bank = 12,000 + (12000)(0.05)(20) = 24,000 Centura Bank = 12,000 (1.05)^20 = 12,000 (2.65329770514) = 31,839.57 31,839.57 - 24,000 = 7,839.57 Planters Bank = FV = PV + (PV)(r)(t) Centura Bank = FV = PV (1 + r) ^t

Assume that you just invested $10,968 in an investment account for your new-born child's college fund. Your goal is to grow the fund to $100,000 in 18 years. What is the required average rate of return per year from this account necessary to achieve your goal? (Note: type in your answer as a decimal. For example, if your answer is 12.52%, type in "0.1252".)

0.1306 r = (100,000 / 10,986) ^(1/18) - 1 r = 1.130643 - 1 r = 0.13643 ~ 0.1306 r = (FV / PV) ^(1/t) - 1

Assume that you just invested $10,723 in an investment account for your new-born child's college fund. Your goal is to grow the fund to $100,000 in 18 years. What is the required average rate of return per year from this account necessary to achieve your goal? (Note: type in your answer as a decimal. For example, if your answer is 12.52%, type in "0.1252".)

0.1321 r = (100,00 / 10,723)^(1/18) - 1 r = 1.13206486291 - 1 r = 0.13206486291 ~ 0.1321 r = (FV/PV)^(1/t) - 1

Assume that you just invested $10,132 in an investment account for your new-born child's college fund. Your goal is to grow the fund to $100,000 in 18 years. What is the required average rate of return per year from this account necessary to achieve your goal? (Note: type in your answer as a decimal. For example, if your answer is 12.52%, type in "0.1252".)

0.1356 r = (100,000 / 10,132)^(1/18) - 1 r = (FV / PV)^(1/t) - 1

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?

10.00 percent r = (285,000 / 35,000) ^(1/22) - 1 r = 1.10000537246 - 1 r = 0.10000537246 ~ 0.10000 ~ 10.00% r = (FV/PV)^1/t - 1

Which one of the following is a correct statement, all else held constant? - The present value is directly related to the interest rate. - The present value is inversely related to the future value. - The future value is directly related to the interest rate. - The period of time is directly related to the interest rate. - The future value is inversely related to the period of time.

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? - She will have to wait longer if she earns 6 percent compound interest instead of 6 percent simple interest. - The length of time she has to wait to reach her goal is directly related to the interest rate she earns. - The period of time she has to wait until she reaches her goal is unaffected by the compounding of interest. - The lower the rate of interest she earns, the shorter the time she will have to wait to reach her goal. - The period of time she has to wait decreases as the amount she invests today increases.

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: - discounted interest. - simple interest. - interest on interest. - complex interest. - compound interest.

compound 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: - indexing. - duplicating. - multiplying. - compounding. - discounting.

compounding

The interest rate used to compute the present value of a future cash flow is called the: - current rate. - simple rate. - compound rate. - discount rate. - prime rate.

discount rate.

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 4 years, he will:

earn $27.89 less than if he had invested with his credit union. CUSI = 4,800 + (4,800)(4)(0.04) CUSI = 4,800 + 768 CUSI = 5,568 CBCI = 4,800(1.0365)^4 CBCI = 5540.11 5,568 - 5540.11 = 27.89

Martha is investing $5 today at 6 percent interest so she can have $10 later. The $10 is referred to as the: - present value. - true value. - discounted value. - complex value. - future value.

future value.

Given an interest rate of zero percent, the future value of a lump sum invested today will always: - remain constant, regardless of the investment time period. - be equal to $0. - decrease if the investment time period is lengthened. - be infinite in value. - decrease if the investment time period is shortened.

remain constant, regardless of the investment time period.