Chapter 5 Financial Management

Your bank pays 1.2 percent compounded daily on its savings accounts. If you deposit $7,500 today, how much will you have in your account 15 years from now? A) $8,979.10 B) $9,714.06 C) $9,414.14 D) $9,336.81 E) $8,204.50

A

The interest earned on both the initial principal and the interest reinvested from prior periods is called: A) free interest. B) compound interest. C) simple interest. D) dual interest. E) interest on interest.

B

Sophia and Mallory are the same age. At age 25, Sophia invests $6,000 at 7 percent, compounded annually. At age 30, Mallory invests $6,000 at 7 percent, compounded annually. All else constant, when they both reach age 60: a) they must wait 10 more years to have equal amounts of savings. b) Sophia will have more money than Mallory. C) Mallory will earn more compound interest than Sophia. D) Mallory will earn more interest on interest than Sophia. E) Sophia will have less money when she retires than Mallory.

b

Which one of the following statements concerning interest rates is correct? A) For any positive rate of interest, the annual percentage rate will always exceed the effective annual rate. B) The effective annual rate equals the annual percentage rate when interest is compounded annually. C) Borrowers would prefer monthly compounding over annual compounding given the same annual percentage rate. D) Savers would prefer annual compounding over monthly compounding given the same annual percentage rate. E) The effective annual rate decreases as the number of compounding periods per year increases.

B

You grandfather invested $16,600 years ago to provide annual payments of $700 a year to his heirs forever. What is the rate of return? A) 4.33% B) 4.22% C) 3.65% D) 4.25% E) 4.10%

B

Which one of the following statements related to annuities and perpetuities is correct? A) A perpetuity comprised of $100 monthly payments is worth more than an annuity of $100 monthly payments provided the discount rates are equal. B) Perpetuities are finite but annuities are not. C) Most loans are a form of a perpetuity. D) The present value of a perpetuity cannot be computed but the future value can. E) An ordinary annuity is worth more than an annuity due given equal annual cash flows for 10 years at 7 percent interest compounded annually.

A

You borrowed $185,000 for 30 years to buy a house. The interest rate is 4.35 percent compounded monthly. If you pay all of your monthly payments as agreed, how much total interest will you pay on this mortgage? (Round the monthly payment to the nearest whole cent.) A) $146,542 B) $150,408 C) $147,027 D) $141,406 E) $154,319

A

Suppose the first comic book of a classic series was sold in 1954. In 2020, the estimated price for this comic book was $310,000, which is an annually compounded return of 22 percent. For this to be true, what was the original price of the comic book in 1954? A) $1.00 B) $.62 C) $1.33 D) $.97 E) $1.20

B

Sixty years ago, your grandmother invested $4,500. Today, that investment is worth $430,065.11. What is the average annually compounded rate of return she earned on this investment? A) 10.40% B) 7.90% C) 6.67% D) 11.71% E) 12.02%

B

You are considering two savings options. Both options offer a rate of return of 8.3 percent. The first option is to save $1,500, $1,250, and $6,400 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? A) $11,428 B) $7,489 C) $11,623 D) $7,203 E) $8,449

B

You just invested $49,000 that you received as an insurance settlement. How much more will this account be worth in 40 years if you earn an average return of 7.6 percent rather than 7.1 percent? (Assume annual compounding.) A) $59,818.92 B) $155,986.70 C) $140,423.33 D) $98,509.16 E) $138,342.91

B

Your local pawn shop lends money at an annual rate of 24 percent compounded weekly. What is the effective annual rate being charged on these loans? A) 25.16% B) 27.05% C) 26.49% D) 28.64% E) 27.56%

B

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? A) You should accept the payments because they are worth $202,414 to you today. B) You should accept the payments because they are worth $201,210 to you today. C) You should accept the $200,000 because the payments are only worth $195,413 to you today. D) You should accept the $200,000 because the payments are only worth $189,311 to you today. E) You should accept the payments because they are worth $201,846 to you today

C

Caroline is going to receive a award of $20,000 six years from now. Jiexin is going to receive an award of $20,000 nine years from now. Which one of the following statements is correct if both individuals apply a discount rate of 7 percent? A) In future dollars, Jiexin's award is worth more than Caroline's award. B) Jiexin's award is worth more today than Caroline's award. C) In today's dollars, Caroline's award is worth more than Jiexin's. D) The present values of Caroline's and Jiexin's awards are equal. E) Twenty years from now, the value of Caroline's award will equal the value of Jiexin's award.

C

Jonathan invested $6,220 in an account that pays 11 percent simple interest. How much money will he have at the end of 40 years? A) $408,671 B) $159,654 C) $33,588 D) $404,305 E) $106,905

C

You just obtained a loan of $17,200 with monthly payments for three years at 5.5 percent interest compounded monthly. What is the amount of each payment? A) $1,107.10 B) $439.96 C) $519.37 D) $467.43 E) $1,995.70

C

A credit card company quotes you an APR of 18.9 percent. What is the actual rate of interest you are paying if interest is computed monthly? A) 20.72% B) 18.90% C) 19.21% D) 20.63% E) 19.57%

D

Andrew just calculated the present value of a $15,000 bonus he will receive next year. The interest rate he used in his calculation is referred to as the: A) current yield. B) simple rate. C) compound rate. D) discount rate. E) effective rate.

D

Howell Corporation deposited $12,000 in an investment account one year ago for the purpose of buying new equipment. 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 and plans to purchase the equipment four years from today. Assuming an interest rate of 5.5 percent, how much cash will be available when the company is ready to buy the equipment? A) $47,138.09 B) $43,609.77 C) $45,208.61 D) $46,008.30 E) $44,007.50

D

Island News purchased a piece of property for $2 million. The firm paid a down payment of 20 percent in cash and financed the balance. The loan terms require monthly payments for 25 years at an APR of 5.5 percent compounded monthly. What is the amount of each mortgage payment? A) $88,000.01 B) $67,883.07 C) $9,253.92 D) $9,825.40 E) $12,281.75

D

When you retire 45 years from now, you want to have $1.25 million saved. You think you can earn an average of 7.6 percent, compounded annually, on your investments. To meet your goal, you are trying to decide whether to deposit a lump sum today, or to wait and deposit a lump sum five years from today to fund this goal. How much more will you have to deposit if you wait for five years before making the deposit? A) $19,891.11 B) $17,414.14 C) $21,319.47 D) $20,468.85 E) $13,406.78

D

Which one of the following statements related to loan interest rates is correct? A) The more frequent the compounding period, the lower the effective annual rate given a fixed annual percentage rate. B) Lenders are most apt to quote the effective annual rate. C) The annual percentage rate considers the compounding of interest. D) When comparing loans you should compare the effective annual rates. E) Regardless of the compounding period, the effective annual rate will always be higher than the annual percentage rate.

D

You are comparing two investment options that each pay 6 percent interest compounded annually. Both options will provide you with $12,000 of income. Option A pays $2,000 the first year followed by two annual payments of $5,000 each. Option B pays three annual payments of $4,000 each. Which one of the following statements is correct given these two investment options? Assume a positive discount rate. (No calculations needed.) A) Option A has the higher future value at the end of Year 3. B) Option B is a perpetuity. C) Option A is an annuity. D) Option B has a higher present value at Time 0. E) Both options are of equal value since they both provide $12,000 of income.

D

Claire's coin collection contains fifty 1948 silver dollars. Her grandparents purchased them at their face value in 1948. These coins have appreciated by 7.6 percent annually. How much is the collection expected to be worth in 2025? A) $13,611.18 B) $14,122.01 C) $18,987.56 D) $11,218.27 E) $14,077.16

E

Twenty-five years from now, you would like to give your child $100,000. How much money must you set aside today if you can earn 7.5 percent per year, compounded annually, on your investment? A) $16,817.67 B) $15,911.13 C) $15,388.19 D) $17,488.37 E) $16,397.91

E

You're trying to save to buy a new $68,000 sports car. Currently, you have saved $36,840 which is invested at 4.9 percent annually compounded interest. How many years will it be before you purchase the car, assuming the price of the car remains constant? A) 10.84 years B) 16.91 years C) 9.67 years D) 17.18 years E) 12.81 years

E