Finance Chapter 4 HW Review

An annuity costs $70,000 today, pays $3,500 per year, and earns a return of 4.5 percent. What is the length of the annuity time period?

52.31 years $70,000 = $3,500[(1 − 1/1.045^T)/.045] 10 = 1.045^T ln10 = Tln1.045 T = 52.31 years

Assume a project has an initial cash outflow followed by seven years of cash inflows. If the discount rate increases, the present value will:

decrease

Your credit card company charges you 1.35 percent per month. What is the annual percentage rate on your account?

16.20% APR = .0135(12) APR = .1620, or 16.20%

You want to establish a charitable trust that will provide $50,000 per year forever to a particular charity. If the fund can earn a guaranteed rate of return of 4.5 percent, how much must you deposit in a solitary lump sum to establish this trust?

$1,111,111 PV = $50,000/.045 PV = $1,111,111

Kwame is willing to pay $185 per month for four years for a car payment. If the interest rate is 4.9 percent per year, compounded monthly, and he makes a cash down payment of $2,500, what price car can he afford to purchase?

$10,549.07 PV = $2,500 + $185{[1 − 1/(1 + .049/12)4(12)]/(.049/12)}PV = $10,549.07

Assume you deposited $3,200 in an account two years ago and are depositing another $5,000 today. You will make a final deposit of $3,500 one year from now. What will your account balance be three years from now if the account pays 4.85 percent interest, compounded annually?

$13,666.10 FV3 = $3,200(1.04855) + $5,000(1.04853) + $3,500(1.04852) FV3 = $13,666.10

Mo will receive a perpetuity of $23,000 per year forever, while Curly will receive the same annual payment for the next 45 years. If the interest rate is 6.7 percent, how much more are Mo's payments worth?

$18,546.17 PV = $23,000/.067 = $343,283.58 PV = $23,000[1 − (1/1.067045)/.0670] = $324,737.42 Difference = $343,283.58 − 324,737.42 = $18,546.17

Leo received $7,500 today and will receive another $5,000 two years from today. If he invests these funds immediately at 11.5 percent, what will his investment be worth five years from now?

$19,856.13 FV = $7,500(1.1155) + $5,000(1.1153) FV = $19,856.13

You have been awarded an insurance settlement of $211,400 that is payable one year from today. What is the minimum amount you should accept today in exchange for this settlement if you can earn 6.3 percent on your investments?

$198,871.12 PV = $211,400/1.063 PV = $198,871.12

Zhu Equity established a trust fund that provides $125,000 in college scholarships each year. The trust fund earns 6.15 percent and distributes only its annual income. How much money did Zhu contribute to establish this fund?

$2,032,520 PV = $125,000/.0615 PV = $2,032,520

Marko, Inc., is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $4,700, $9,700, and $15,900 over the next three years, respectively. After that time, they feel the business will be worthless. Marko has determined that a rate of return of 12 percent is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.?

$23,246.52 PV = $4,700/(1 + .12) + $9,700/(1.12)2 + $15,900/(1.12)3 = $23,246.52 CFo = 0 C01 = 4,700 F01 = 1 C02 = 9,700 F02 = 1 C03 = $15,900 F03 = 1 I = 12

One year ago, the Jenkins Family Fun Center deposited $3,900 into an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $5,700 to this account. They plan on making a final deposit of $7,900 to the account next year. How much will be available when they are ready to buy the equipment, assuming they earn a rate of return of 8 percent?

$23,436.89 FV = $3,900 (1 + 0.08)5 + $5,700 (1 + 0.08)4 + $7,900 (1 + 0.08)3 = $23,436.89

Ryan saves $3,000 per year at an interest rate of 4.2 percent. What will his savings be worth at the end of 35 years?

$230,040.06 FV = $3,000[(1.042^35 − 1)/.042] FV = $230,040.06

You need to have $30,000 for a down payment on a house in 6 years. If you can earn an annual interest rate of 3.6 percent, how much will you have to deposit today?

$24,264.02 PV = $30,000/1.0366 = $24,264.02 n= 6 FV= -30,000 i/y= 3.6%

You have just started a new job and plan to save $4,650 per year for 43 years until you retire. You will make your first deposit in one year. How much will you have when you retire if you earn an annual interest rate of 10.31 percent?

$3,021,337.12 FV = $4,650[1.103143 − 1)/.1031] = $3,021,337.12

Assume your employer will contribute $50 per week for twenty years to your retirement plan. At a discount rate of 5 percent, compounded weekly, what is this employee benefit worth to you today?

$32,861.08 PV = $50{[1 − 1/(1 + .05/52)^20(52)]/(.05/52)} PV = $32,861.08

Starting today, Hector is going to contribute $100 per month to his retirement account. His employer will make matching contributions equal to 50 percent of Hector's contributions. If the total contributions remain constant, and he earns a monthly rate of .55 percent, how much will his savings be worth 40 years from now?

$352,151.04 FVA = $150[(1 + .0055)^480 - 1]/ .0055

Assume you graduate with $26,800 in student loan debt at an interest rate of 4.25 percent, compounded monthly. If you want to have this debt paid in full within seven years, how much must you pay each month?

$369.42 $26,800 = C{[1 − 1/(1 + .0425/12)^7(12)]/(.0425/12)} C = $369.42

Assume you borrowed $19,600 to buy a car. The terms of the loan call for monthly payments for five years at an interest rate of 6.25 percent, compounded monthly. What is the amount of each payment?

$381.21 $19,600 = C{[1 − 1/(1 + .0625/12)^5(12)]/(.0625/12)} C = $381.21

Marco invested $50,000 in account that he predicts will earn 5.25 percent per year, compounded annually. What does he expect his account to be worth in 45 years?

$499,994 FV5 = $50,000(1.052545) FV5 = $499,994

What is the future value of $3,118 invested for 10 years at 6.4 percent compounded annually?

$5,798.19 FV = $3,118 × 1.06410 = $5,798.19 n is 10 i/y = 6.4% pv = −$3,118

You expect an investment to return $11,300, $14,600, $21,900, and $38,400 annually over the next four years, respectively. What is this investment worth to you today if you desire a rate of return of 16.5 percent?

$55,153.57 PV = $11,300/1.165 + $14,600/1.165^2 + $21,900/1.165^3 + $38,400/1.165^4 PV = $55,153.57

On the day she retired, Kate had $101,900 in retirement savings. She expects to earn 4.5 percent, compounded monthly, and live 24 more years. How much can she withdraw from her savings each month during her retirement if she plans to die on the day she spends her last penny?

$579.22 $101,900 = C{[1 − 1/(1 + .045/12)^24(12)]/(.045/12)} C = $579.22

Your parents are giving you $160 a month for 4 years while you are in college. At an interest rate of .39 percent per month, what are these payments worth to you when you first start college?

$6,991.60 PV = $160[(1 −1/1.00394×12)/.0039] = $6,991.60

Beatrice invests $1,360 in an account that pays 3 percent simple interest. How much more could she have earned over a 4-year period if the interest had been compounded annually?

$7.49 Balance Year 4 with simple interest = $1,360 + ($1,360 × 0.03 × 4) = $1,523.20Balance Year 4 with compound interest = $1,360 × 1.034 = $1,530.69Additional interest = $1,530.69 − $1,523.20 = $7.49

What is the future value of $845 per year for seven years at an interest rate of 11.3 percent?

$8,343.51 FV = $845[(1.113^7 − 1)/.113] FV = $8,343.51

Starling wants to retire with $2,050,000 in his retirement account exactly 35 years from today. He will make annual deposits at the end of each year to fund his retirement account. If he can earn 9.49 percent per year, how much must he deposit each year?

$8,501.38 $2,050,000 = C[(1.094935 − 1)/.0949] C = $8,501.38

Your parents plan to give you $200 per month for four years while you are in college. At a discount rate of 6 percent, compounded monthly, what are these payments worth to you when you first start college?

$8,516.06 PV = $200{[1 − 1/(1 + .06/12)^4(12)]/(.06/12)} PV = $8,516.06

You want to buy a house and will need to borrow $185,000. The interest rate on your loan is 5.05 percent compounded monthly and the loan is for 30 years. What are your monthly mortgage payments?

$998.78 $185,000 = C[1 − (1/(1 + .0505/12)360)/(.0505/12)] C = $998.78 n= 30x12 i/y = 5.05%/12 PV = −$185,000

What is the effective annual rate for an APR of 12.20 percent compounded quarterly?

12.77% EAR = (1 + .1220/4)4 - 1 = .1277, or 12.77%

Maxxie purchased a tract of land for $25,500. Today, the same land is worth $58,300. How many years have passed if the price of the land has increased at an annual rate of 6.5 percent?

13.13 years $58,300 = $25,500(1.065)^t t = 13.13 years

You are retired, have $264,500 in your savings, withdraw $2,000 each month, and earn 4.5 percent, compounded monthly. How long will it be until you run out of money?

15.25 years $264,500 = $2,000{[1 − 1/(1 + .045/12)^T]/(.045/12)} ln1.9839 = Tln1.00375 T = 183.02 months, or 15.25 years

Several years ago, Jacquelyn invested $6,000. Today, that investment is worth $97,920. It has earned an average annual rate of return of 9.5 percent, compounded annually. How long ago did Jacquelyn make her investment?

30.77 years $97,920 = $6,000(1.095)^T ln16.32 = ln1.095T T = 30.77 years

You just paid $525,000 for a security that will pay you and your heirs $25,000 per year forever. What rate of return will you earn?

4.76% r = $25,000/$525,000 r = .0476, or 4.76%

You are borrowing $5,200 at 7.8 percent, compounded monthly. The monthly loan payment is $141.88. How many loan payments must you make before the loan is paid in full?

42 $5,200 = $141.88{[1 − 1/(1 + .078/12)^T]/(.078/12)} ln1.3127 = Tln1.0065 T = 42

When your father was born 47 years ago, his grandparents deposited $175 in an account for him. Today, that account is worth $1,900. What was the annual rate of return on this account?

5.21 percent $1,900 = $175(1 + r)^47 r = ($1,900/$175)^1/47 − 1 r = .0521, or 5.21%

If you invest $15,000 today, an investment guarantees that 24 years from today you will have $54,750. What annual rate of interest will you earn?

5.54% $54,750 = $15,000(1 + r)^24 r = .0554, or 5.54%

*You want to have $2.85 million when you retire in 40 years. You feel that you can save $700 per month until you retire. What APR do you have to earn in order to achieve your goal?

8.53% $2,850,000 = $700{[(1 + r)480 − 1] / r} r = .0071, or .71% r = .71% × 12 = 8.53%

Aubrey just purchased an annuity that will pay $2,500 per month for five years. The first payment was issued today. Bennett just purchased an annuity that will pay $2,500 per month for five years. The first payment will be issued one month from today. Which one of the following statements is correct concerning these two annuities?

Aubrey's annuity has a higher present value than Bennett's.

You have $2,500 to deposit into a savings account. The five banks in your area offer the following rates. In which bank should you deposit your savings?

Bank B: 3.69%, compounded monthly EARBank A = 3.75% EARBank B = (1 + .0369/12)^12 − 1EAR Bank B = .03753, or 3.753% EARBank C = (1 + .0370/2)^2 − 1 EARBank C = .03734, or 3.734% EARBank D = e.0367 − 1EAR Bank D = .03738, or 3.738% EARBank E = (1 + .0365/4)^4 − 1 EARBank E = .03700, or 3.700% Bank B offers the highest EAR.

________ annuities have payments that occur at the end of each period, whereas ________ annuities have payments that occur at the beginning of each period.

Ordinary annuities; annuities due

Sanghyuk will receive payments of $550 per month for ten years. What are these payments worth today at a discount rate of 6 percent, compounded monthly?

PV = $550{[1 − 1/(1 + .06/12)^10(12)]/(.06/12)} PV = $49,540.40

You would be making a wise decision if you chose to: a. base decisions regarding investments on effective rates and base decisions regarding loans on annual percentage rates. b. assume all loans and investments are based on simple interest. accept the loan with the lower effective annual rate rather than the loan with the lower annual percentage rate. c. invest in an account paying 6 percent, compounded quarterly, rather than an account paying 6 percent, compounded monthly. d. ignore the effective rates and concentrate on the annual percentage rates for all transactions.

accept the loan with the lower effective annual rate rather than the loan with the lower annual percentage rate.

Ramirez Wellness borrowed $150,000 for five years and is now making monthly payments that include both principal and interest. Paying off the debt by making installment payments, such as this firm is doing, is referred to as:

amortizing the debt amortization - the action or process of reducing or paying off a debt with regular payments.

The ________ rate equals the interest rate per period multiplied by the number of periods per year.

annual percentage

An interest rate that is compounded monthly, but is expressed as if the rate were compounded annually, is called the ________ rate.

effective annual