FIN 3403 Chapter 6

You are going to loan a friend $6,000 for one year at an interest rate of 4.5 percent, compounded annually. How much additional interest could you have earned if you had compounded the rate continuously rather than annually?

$.6.17

Waldo expects to receive the following payments: year 1 = $50,000; year 2 = $28,000; year 3 = $12,000. All of this money will be saved for his retirement. If he can earn an average annual return of 10.5 percent, how much will he have in his account 25 years after making the first deposit?

$1,033,545

You want to buy a new sports car for $55,000. The contract is in the form of a 60-month annuity due at an APR of 6 percent, compounded monthly. What will be your monthly payment?

$1,058.01

Nadine is retiring today at age 66 and expects to live to age 82. She has $136,000 in her retirement savings account. She is somewhat conservative with her money and expects to earn 6 percent during her retirement years. How much can she withdraw from her retirement savings each month if she plans to spend her last penny on the morning of her death?

$1,103.56

On the day you entered college, you borrowed $25,000 on an interest-only, four-year loan at 4.75 percent from your local bank. Payments are to be paid annually. What is the amount of your loan payment in year 2?

$1,187.50

Goods Guys Foods established a trust fund that provides $125,000 in scholarships each year for needy students. The trust fund earns a fixed 7.25 percent rate of return. How much money did the firm contribute to the fund assuming that only the interest income is distributed?

$1,724,138

You are borrowing money today at 8.48 percent, compounded annually. You will repay the principal plus all the interest in one lump sum of $12,800 two years from today. How much are you borrowing?

$10,877.04

Phil can afford $240 a month for five years for a car loan. If the interest rate is 8.5 percent, how much can he afford to borrow to purchase a car?

$11,697.88

You just signed a consulting contract that will pay you $38,000, $52,000, and $85,000 annually at the end of the next three years, respectively. What is the present value of these cash flows given a discount rate of 10.5?

$139,975

Trish receives $450 on the first of each month. Josh receives $450 on the last day of each month. Both Trish and Josh will receive payments for next four years. At a discount rate of 9.5 percent, what is the difference in the present value of these two sets of payments?

$141.80

You borrow $230,000 to buy a house. The mortgage rate is 4.5 percent and the loan period is 25 years. Payments are made monthly. If you pay the mortgage according to the loan agreement, how much total interest will you pay?

$153,524

This morning, you borrowed $13,400 at a 6.9 percent annual interest rate. You are to repay the loan principal plus all of the loan interest in one lump sum three years from today. How much will you have to repay?

$16,369.59

You need some money today and the only friend you have that has any is your miserly friend. He agrees to loan you the money you need, if you make payments of $30 a month for the next six months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 2 percent interest per month. How much money are you borrowing?

$171.40

Jones Stoneware has a $65,000 liability it must pay four years from today. The company is opening a savings account so that the entire amount will be available when this debt comes due. The plan is to make an initial deposit today and then deposit an additional $10,000 at the end of each of the four years. The account pays a 4.5 percent rate of return. How much does the firm need to deposit today?

$18,631.23

Western Bank offers you a $10,000, 6-year term loan at 7 percent annual interest. What is the amount of your annual loan payment?

$2,097.96

You are scheduled to receive annual payments of $3,600 for each of the next 12 years. The discount rate is 8 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

$2,170.39

The present value of the following cash flow stream is $5,933.86 when discounted at 11 percent annually. What is the value of the missing cash flow? Year Cash Flow 1 $2,000 2 ? 3 1,750 4 1,250

$2,500

You would like to establish a trust fund to provide $140,000 a year forever for your heirs. The expected rate of return is 5.45 percent. How much money must you deposit today to fund this gift?

$2,568,807

You need a 30-year, fixed-rate mortgage to buy a new home for $225,000. Your bank will lend you the money at an APR of 5.5 percent with monthly compounding. You can only afford monthly payments of $1,000 for principal and interest, so you offer to pay off any remaining loan balance at the end of the loan term in the form of a single balloon payment. What will be the amount of the balloon payment?

$253,550

You are buying a pre-owned car today at a price of $8,500. You are paying $300 down in cash and financing the balance for 36 months at 7.75 percent. What is the amount of each monthly loan payment?

$256.01

Beginning three months from now, you want to be able to withdraw $1,700 each quarter from your bank account to cover college expenses. The account pays .45 percent interest per quarter. How much do you need to have in your account today to meet your expense needs over the next four years?

$26,187.10

Stephanie is going to contribute $250 on the first of each month, starting today, to her retirement account. Her employer will provide a 50 percent match. In other words, her employer will add $125 to the amount Stephanie saves. If both Stephanie and her employer continue to do this and she can earn a monthly interest rate of .5 percent, how much will she have in her retirement account 25 years from now?

$261,172

Your great aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $2,400 on the first day of each year, starting immediately and continuing for 20 years. What is the value of this inheritance today if the applicable discount rate is 6.75 percent?

$27,677.34

The government has imposed a fine on JJ's Place. The fine calls for annual payments of $60,000, $70,000, $75,000, and $50,000, respectively, over the next four years. The first payment is due one year from today. The government plans to invest the funds until the final payment is collected and then donate the entire amount, including the investment earnings, to help the local community shelter. The government will earn 5.5 percent on the funds held. How much will the community shelter receive four years from today?

$277,491

Your parents have made you two offers. The first offer includes annual gifts of $10,000, $11,000, and $12,000 at the end of each of the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 8 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer?

$28,216

Your employer contributes $60 a week to your retirement plan. Assume you work for your employer for another 20 years and the applicable discount rate is 9 percent. Given these assumptions, what is this employee benefit worth to you today?

$28,927.38

You want to be a millionaire when you retire in 40 years and can earn an annual return of 12.5 percent. How much more will you have to save each month if you wait 15 years to start saving versus if you start saving at the end of this month?

$414.34

Racing Engines wants to save $750,000 to buy some new equipment four years from now. The plan is to set aside an equal amount of money on the first day of each quarter starting today. The firm can earn 4.75 percent on its savings. How much does the firm have to save each quarter to achieve its goal?

$42,337.00

An insurance annuity offers to pay you $1,000 per quarter for 20 years. If you want to earn a rate of return of 6.5 percent, what is the most you are willing to pay as a lump sum today to buy this annuity?

$44,591.11

A wealthy benefactor just contributed to your college's scholarship program. This gift will provide $20,000 in scholarships next year with that amount increasing by 2 percent annually thereafter.. If the discount rate is 6.5 percent, what is the current value of this perpetual gift?

$444,444

You are borrowing $21,800 to buy a car. The terms of the loan call for monthly payments for five years at 8.25 percent interest. What is the amount of each payment?

$444.64

You are considering a project that will provide annual cash inflows of $16,500, $25,700, and $18,000 at the end of each year for the next three years, respectively. What is the present value of these cash flows, given a discount rate of 12.5 percent?

$47,615

You are considering two savings options. Both options offer a rate of return of 11 percent. The first option is to save $2,500, $1,500, and $3,000 at the end of each year for the next three years, respectively. The other option is to save one lump sum amount today. You want to have the same balance in your savings account at the end of the three years, regardless of the savings method you select. If you select the lump sum method, how much do you need to save today?

$5,663.26

Southern Tours is considering acquiring Holiday Vacations. Management believes Holiday Vacations can generate cash flows of $187,000, $220,000, and $245,000 over the next three years, respectively. After that time, they feel the business will be worthless. If the desired rate of return is 13.5 percent, what is the maximum Southern Tours should pay today to acquire Holiday Vacations?

$503,098

One year ago, JK Mfg. deposited $20,500 in an investment account for the purpose of buying new equipment four years from today. Today, it is adding another $15,000 to this account. The company plans on making a final deposit of $10,000 to the account one year from today. How much will be available when it is ready to buy the equipment, assuming the account pays 3.5 interest?

$52,648

John's Auto Repair just took out a $52,000, 10-year, 8 percent, interest-only loan from the bank. Payments are made annually. What is the amount of the loan payment in year 10?

$56,160

Your car dealer is willing to lease you a new car for $190 a month for 36 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 6.5 percent, what is the current value of the lease?

$6,232.80

On June 1, you borrowed $195,000 to buy a house. The mortgage rate is 5.25 percent. The loan is to be repaid in equal monthly payments over 15 years. All taxes and insurance premiums are to be paid separately. The first payment is due on July 1. How much of the first payment applies to the principal balance?

$714.43

Travis International has a one-time expense of $2.86 million that must be paid three years from now. Since the firm cannot raise that amount in one day, it wants to save an equal amount each month over the next three years to fund this expense. If the firm can earn 2.1 percent on its savings, how much must it save each month?

$77,037.69

Your broker is offering 1.2 percent compounded daily on its money market account. If you deposit $7,500 today, how much will you have in your account 15 years from now?

$8,979.10

Rosina plans on saving $2,000 a year and expects to earn an annual rate of 8.8 percent. How much will she have in her account at the end of 43 years?

$831,532

You just won the grand prize in a national writing contest! As your prize, you will receive $1,000 a month for 10 years. If you can earn 7 percent on your money, what is this prize worth to you today?

$86,126.35

The Friendly Bank wants to earn an effective annual return on its consumer loans of 12 percent per year. The bank uses daily compounding. What rate is the bank most apt to quote on these loans?

11.33 percent

Jogging Gear is considering a project with an initial cash requirement of $238,400. The project will yield cash flows of $4,930 monthly for 65 months. What is the rate of return on this project?

11.38 percent

Today, you are retiring. You have a total of $289,416 in your retirement savings. You want to withdraw $2,500 at the beginning of every month, starting today and expect to earn 4.6 percent, compounded monthly. How long will it be until you run out of money?

12.71 years

You are paying an effective annual rate of 15.33 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate on this account?

14.35 percent

You are considering an annuity that costs $160,000 today. The annuity pays $17,500 a year at an annual interest rate of 7.5 percent. What is the length of the annuity time period?

16 years

What is the effective annual rate of 14.9 percent compounded continuously?

16.07 percent

Your local pawn shop loans money at an annual rate of 23 percent and compounds interest weekly. What is the actual rate being charged on these loans?

25.80 percent

You just received an offer in the mail to transfer your $5,000 balance from your current credit card, which charges an annual rate of 18.7 percent, to a new credit card charging a rate of 5.9 percent. You plan to make payments of $250 a month on this debt. How many fewer payments will you have to make to pay off this debt if you transfer the balance to the new card?

3.05 payments

You grandfather invested $20,000 years ago to provide annual payments of $750 a year to his heirs forever. What is the rate of return?

3.75 percent

MBM estimates its expansion cost at $18.63 million and wants it fully funded upfront. Management has decided to save $1.1 million a quarter for this purpose. The firm earns 6.25 percent, compounded quarterly, on its savings. How long does the firm have to wait before expanding its operations?

3.79 years

You just paid $750,000 for an annuity that will pay you and your heirs $36,000 a year forever. What rate of return are you earning on this policy?

4.80 percent

Your father helped you start saving $20 a month beginning on your fifth birthday. He always made you deposit the money into your savings account on the first day of each month just to "start the month out right." Today completes your 17th year of saving and you now have $6,528.91 in this account. What is the rate of return on your savings?

5.15 percent

Today, you borrowed $6,200 on your credit card to purchase some furniture. The interest rate is 14.9 percent, compounded monthly. How long will it take you to pay off this debt assuming that you do not charge anything else and make regular monthly payments of $120?

6.93 years

You want to buy a new sports coupe for $41,750 and the finance office at the dealership has quoted you an APR of 7.6, compounded monthly for 48 months. What is the effective interest rate on this loan?

7.87 percent

First City Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.65 percent annual percentage rate on its loans. What is the maximum rate the bank can actually earn based on the quoted rate?

7.95 percent

Today, you turn 23. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $75 a day, every day, until you turn 40. You open an investment account and deposit your first $75 today. What rate of return must you earn to achieve your goal?

8.09 percent

Al's obtained a discount loan of $71,000 today that requires a repayment of $90,000, 3 years from today. What is the APR on this loan?

8.23 percent

On this date last year, you borrowed $3,400. You have to repay the loan principal plus all of the interest six years from today. The payment that is required at that time is $6,000. What is the interest rate on this loan?

8.45 percent

You have been investing $250 a month for the last 13 years. Today, your investment account is worth $73,262. What is your average rate of return on your investments?

8.94 percent

You want to borrow $38,400 and can afford monthly payments of $960 for 48 months, but no more. Assume monthly compounding. What is the highest APR rate you can afford?

9.24 percent

The banks in your area offer the following rates of interest on their savings accounts. If you want to open one of these accounts, which bank should you select? Bank A: .75 percent APR with daily compounding. Bank B: .85 percent APR with monthly compounding. Bank C: .8725 percent APR with annual compounding. Bank D: .87 percent APR with quarterly compounding. Bank E: .775 percent APR with semiannual compounding.

Bank D

You are considering five loan offers. The only significant difference between them is their interest rates. Given the following information, which offer should you accept? (Assume a 365-day year.) Offer A: 6.75 percent APR with daily compounding. Offer B: 6.8 percent APR with monthly compounding. Offer C: 7 percent APR with annual compounding. Offer D: 6.825 percent APR with quarterly compounding. Offer E: 6.85 percent APR with semiannual compounding.

Offer E

You just received an insurance settlement offer related to an accident you had three years ago. The offer provides you with three choices: Option A: $1,500 a month for 6 years Option B: $1,025 a month for 10 years Option C: $85,000 as a lump sum payment today You can earn 7.5 percent on your investments and do not care if you personally receive the funds or if they are paid to your heirs should you die within the settlement period. Which option should you select and why is that option justified?

Option A: It has the greatest value today.

What is the present value of $1,400 a year at a discount rate of 8 percent if the first payment is received 7 years from now and you receive a total of 23 annual payments?

$9,149.74

You are planning a special wedding three years from today. You don't know who your spouse will be but you do know that you are saving $25,000 today and $35,000 one year from today for this purpose. You also plan to pay the final $45,000 of costs on your wedding day. At a discount rate of 7 percent, what is the current cost of your special wedding?

$94,444

Sue plans to save $4,500, $0, and $5,500 at the end of each of the next three years, respectively. What will her investment account be worth at the end of the third year if she earns an annual rate of 4.15 percent?

$10,381.25

You have your choice of two investment accounts. Investment A is a five-year annuity that features end-of-month $2,500 payments and has an interest rate of 11.5 percent compounded monthly. Investment B is a 10.5 percent continuously compounded lump sum investment, also good for five years. How much would you need to invest in B today for it to be worth as much as investment A five years from now?

$119,176.06

Theresa adds $1,500 to her savings account on the first day of each year. Marcus adds $1,500 to his savings account on the last day of each year. They both earn 6.5 percent annual interest. What is the difference in their savings account balances at the end of 35 years?

$12,093

Island News purchased a piece of property for $1.36 million. The firm paid a down payment of 12 percent in cash and financed the balance. The loan terms require monthly payments for 10 years at an annual percentage rate of 4.75 percent, compounded monthly. What is the amount of each mortgage payment?

$12,548.18

What is the future value of $1,400 a year for 35 years at 6 percent interest? Assume annual compounding.

$156,009

You are comparing two annuities with equal present values. The applicable discount rate is 7.25 percent. One annuity pays $2,500 on the first day of each year for 15 years. How much does the second annuity pay each year for 15 years if it pays at the end of each year?

$2,681.25

DLM preferred stock has a 5.8 percent dividend yield. The stock is currently priced at $36.20 per share. What is the amount of the annual dividend?

$2.10

Your grandfather left you an inheritance that will provide an annual income for the next 20 years. You will receive the first payment one year from now in the amount of $16,500. Every year after that, the payment amount will increase by 5 percent. What is your inheritance worth to you today if you can earn 7.5 percent on your investments?

$247,750

You just purchased an annuity that will pay you $24,000 a year for 25 years, starting today. What was the purchase price if the discount rate is 8.5 percent?

$266,498

You are planning to save for retirement over the next 15 years. To do this, you will invest $1,100 a month in a stock account and $500 a month in a bond account. The return on the stock account is expected to be 7 percent, and the bond account will pay 4 percent. When you retire, you will combine your money into an account with a 5 percent return. How much can you withdraw each month during retirement assuming a 20-year withdrawal period?

$3,113.04

You just settled an insurance claim. The settlement calls for increasing payments over a five-year period. The first payment will be paid one year from now in the amount of $7,000. The following payments will increase by 3.5 percent annually. What is the value of this settlement to you today if you can earn 6.5 percent on your investments?

$31,063.79

You are the recipient of a gift that will pay you $25,000 one year from now and every year thereafter for the following 24 years. The payments will increase in value by 2.5 percent each year. If the appropriate discount rate is 8.5 percent, what is the present value of this gift?

$316,172

Troy will receive $7,500 at the end of year 2. At the end of the following two years, he will receive $9,000 and $12,500, respectively. What is the future value of these cash flows at the end of year 5 if the interest rate is 8 percent?

$33,445

You just won the magazine sweepstakes and opted to take unending payments. The first payment will be $21,500 and will be paid one year from today. Every year thereafter, the payments will increase by 2.5 percent annually. What is the present value of your prize at a discount rate of 7.9 percent?

$398,148

You estimate that you will owe $39,950 in student loans by the time you graduate. The interest rate is 3.75 percent. If you want to have this debt paid in full within 10 years, how much must you pay each month?

$399.74

A preferred stock pays an annual dividend of $4.10. What is one share of this stock worth today if the rate of return is 9.68 percent?

$42.36

This morning, you borrowed $162,000 to buy a house. The mortgage rate is 4.35 percent. The loan is to be repaid in equal monthly payments over 20 years with the first payment due one month from today. Assume each month is equal to 1/12 of a year and all taxes and insurance premiums are paid separately. How much of the second payment applies to the principal balance?

$426.11

You want to start your own consulting business and believe it could produce cash flows of $5,600, $48,200, and $125,000 at the end of each of the next three years, respectively. At the end of three years you think you can sell the business for $450,000. At a 14 percent discount rate, what is this business idea worth today?

$430,109

Your grandmother is gifting you $150 a month for four years while you attend college to earn your bachelor's degree. At a 4.8 percent discount rate, what are these payments worth to you on the day you enter college?

$6,539.14

The Distribution Point plans to save $2,000 a month for the next 3 years for future emergencies. The interest rate is 4.5 percent compounded monthly. The first monthly deposit will be made today. What would today's deposit amount have to be if the firm opted for one lump sum deposit that would yield the same amount of savings as the monthly deposits after 3 years?

$67,485.97

On the day you entered college, you borrowed $30,000 from your local bank. The terms of the loan include an interest rate of 4.75 percent. The terms stipulate that the principal is due in full one year after you graduate. Interest is to be paid annually at the end of each year. Assume that you complete college in four years. How much total interest will you pay on this loan assuming you paid as agreed?

$7,125

You just acquired a 30-year mortgage in the amount of $179,500 at 4.75 percent interest, compounded monthly. Payments will be equal over the life of the loan with the first payment due one month after the date of the loan. How much of the first payment will be interest?

$710.52

What is the future value of $12,000 a year for 40 years at 11.5 percent interest?

$8,014,195

You have been purchasing $9,000 worth of stock annually for the past 5 years and now have a portfolio valued at $45,881. What is your annual rate of return?

.97 percent

Your insurance agent is trying to sell you an annuity that costs $50,000 today. By buying this annuity, your agent promises that you will receive payments of $250 a month for the next 20 years. What is the rate of return on this investment?

1.88 percent

You are preparing to make monthly payments of $75, beginning at the end of this month, into an account that pays 6 percent interest compounded monthly. How many payments will you have made when your account balance reaches $10,000?

102

What is the annual percentage rate on a loan with a stated rate of 2.75 percent per quarter?

11.00 percent

What is the effective annual rate of 11.9 percent compounded continuously?

12.64 percent

Your credit card company charges you 1.65 percent interest per month. What is the annual percentage rate on your account?

19.80 percent

Your credit card company quotes you an interest rate of 21.9 percent based on annual compounding. Interest is billed monthly. What is the actual rate of interest you are paying?

24.24 percent

The Art Gallery is notoriously known as a slow-payer. The firm currently needs to borrow $25,000 and only one company will loan to them. The terms of the loan call for weekly payments of $500 at a weekly interest rate of .45 percent. What is the loan term?

56.77 weeks

You have just purchased a new warehouse. To finance the purchase, you arranged for a 30-year mortgage loan for 65 percent of the $2.5 million purchase price. The monthly payment on this loan will be $10,400. What is the effective annual rate on this loan?

6.82 percent

What is the effective annual rate if a bank charges you an APR of 8.25 percent, compounded quarterly?

8.51 percent

You are considering a one-year discount loan of $16,000. The interest rate is quoted as 7 percent plus 4 points. What is the actual rate you are paying on this loan?

11.46 percent

As the beneficiary of a life insurance policy, you have two options for receiving the insurance proceeds. You can receive a lump sum of $200,000 today or receive payments of $1,400 a month for 20 years. If you can earn 6 percent on your money, which option should you take and why?

You should accept the $200,000 because the payments are only worth $195,413 to you today.

You have some property for sale and have received two offers. The first offer is for $89,500 today in cash. The second offer is the payment of $35,000 today and an additional guaranteed $70,000 two years from today. If the applicable discount rate is 11.5 percent, which offer should you accept and why?

You should accept the second offer because it has the larger net present value.