You have determined the profitability of a planned project by finding the present value of all the cash flows from that project. Which of the following would cause the project to look more appealing in terms of the present value of those cash flows?
A. a. The discount rate decreases.
B. b. The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the same.
C. c. The discount rate increases.
D. d. Answers b and c above.
E. e. Answers a and b above.
Which of the following statements is correct?
A. a. The present value of an annuity due will exceed the present value of an ordinary annuity (assuming all else equal).
B. b. The future value of an annuity due will exceed the future value of an ordinary annuity (assuming all else equal).
C. c. The nominal interest rate will always be greater than or equal to the effective annual interest rate.
D. d. Statements a and b are correct.
E. e. All of the statements above are correct.
Frank Lewis has a 30-year, $100,000 mortgage with a nominal interest rate of 10 percent and monthly compounding. Which of the following statements regarding his mortgage is correct?
A. a. The monthly payments will decline over time.
B. b. The proportion of the monthly payment which represents interest will be lower for the last payment than for the first payment on the loan.
C. c. The total dollar amount of principal being paid off each month gets larger as the loan approaches maturity.
D. d. Statements a and c are correct.
E. e. Statements b and c are correct.
Suppose someone offered you the choice of two equally risky annuities, each paying $10,000 per year for five years. One is an ordinary (or deferred) annuity, the other is an annuity due. Which of the following statements is correct?
A. a. The present value of the ordinary annuity must exceed the present value of the annuity due, but the future value of an ordinary annuity may be less than the future value of the annuity due.
B. b. The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value of the annuity due is less than the future value of the ordinary annuity.
C. c. The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of the annuity due also exceeds the future value of the ordinary annuity.
D. d. If interest rates increase, the difference between the present value of the ordinary annuity and the present value of the annuity due remains the same.
E. e. Answers a and d are correct.
Which of the following investments would provide an investor the highest effective annual return?
A. a. An investment which has a 9 percent nominal rate with semiannual compounding.
B. b. An investment which has a 9 percent nominal rate with quarterly compounding.
C. c. An investment which has a 9.2 percent nominal rate with annual compounding.
D. d. An investment which has an 8.9 percent nominal rate with monthly compounding.
E. e. An investment which has an 8.9 percent nominal rate with quarterly compounding
You just put $1,000 in a bank account which pays 6 percent nominal annual interest, compounded monthly. How much will you have in your account after 3 years?
A. a. $1,006.00
B. b. $1,056.45
C. c. $1,180.32
D. d. $1,191.00
E. e. $1,196.68
You just graduated, and you plan to work for 10 years and then to leave for the Australian “Outback” bush country. You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings cash flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you put the gift now, and your future savings when they start, into an account which pays 8 percent compounded annually, what will your financial “stake” be when you leave for Australia 10 years from now?
A. a. $21,432
B. b. $28,393
C. c. $16,651
D. d. $31,148
E. e. $20,000
If you buy a factory for $250,000 and the terms are 20 percent down, the balance to be paid off over 30 years at a 12 percent rate of interest on the unpaid balance, what are the 30 equal annual payments?
A. a. $20,593
B. b. $31,036
C. c. $24,829
D. d. $50,212
E. e. $ 6,667
You are contributing money to an investment account so that you can purchase a house in five years. You plan to contribute six payments of $3,000 a year–the first payment will be made today (t = 0), and the final payment will be made five years from now (t = 5). If you earn 11 percent in your investment account, how much money will you have in the account five years from now (at t = 5)?
A. a. $19,412
B. b. $20,856
C. c. $21,683
D. d. $23,739
E. e. $26,350
If you receive $15,000 today and can invest it at a 5 percent annual rate compounded continuously, what will be your ending value after 20 years?
A. a. $35,821
B. b. $40,774
C. c. $75,000
D. d. $81,342
E. e. $86,750
You decide to begin saving toward the purchase of a new car in 5 years. If you put $1,000 at the end of each of the next 5 years in a savings account paying 4 percent compounded annually, how much will you accumulate after 5 years?
A. a. $1,481.25
B. b. $4,394.51
C. c. $6,592.34
D. d. $5,416.30
E. e. $4,935.35
Calculate the present value of $1,000 to be received at the end of 8 years. Assume an interest rate of 5 percent.
A. a. $1,812.39
B. b. $525.18
C. c. $676.80
D. d. $650.30
E. e. $5,962.31
How much would you be willing to pay today for an investment that would return $800 each year at the end of each of the next 6 years? Assume a discount rate of 4 percent.
A. a. $5,435.89
B. b. $4,398.87
C. c. $4,431.29
D. d. $4,532.21
E. e. $4,193.68
If you would like to accumulate $7,500 over the next 5 years, how much must you deposit each six months, starting six months from now, given a 8 percent interest rate and semiannual compounding?
A. a. $624.69
B. b. $801.22
C. c. $910.16
D. d. $571.32
E. e. $751.56
What is the effective annual percentage rate (EAR) of 12 percent compounded monthly?
A. a. 12.00%
B. b. 12.55%
C. c. 12.68%
D. d. 12.75%
E. e. 13.00%
You have $ 1,000 invested in an account which pays 16 percent compounded annually. A commission agent (called a finder?) can locate for you an equally safe deposit which will pay 16 percent, compounded semi-annually, for 2 years. What is the maximum amount you should be willing to pay him now as a fee for locating the new account?
A. a. $5.63
B. b. $10.95
C. c. $17.15
D. d. $16.94
E. e. $20.15
Assume that your aunt sold her house on December 31 and that she took a mortgage in the amount of $50,000 as part of the payment. The mortgage has a stated (or nominal) interest rate of 10 percent, but it calls for payments every 6 months, beginning on June 30, and the mortgage is to be amortized over 20 years. Now, one year later, your aunt must file Schedule B of her tax return with the IRS informing them of the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) What is the total amount of interest that was paid during the first year?
A. a. $4,979.31
B. b. $683.56
C. c. $2,651.83
D. d. $3,881.78
E. e. $760.52
Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities which call for five payments, $75 at the end of each of the next 4 years, plus a payment of $1,075 at the end of Year 5. Your friend says she can get you some of these securities at a cost of $960 each. Your money is now invested in a bank that pays an 4 percent nominal (quoted) interest rate, but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you?
A. a. $721.93
B. b. $878.96
C. c. $824.51
D. d. $1,532.91
E. e. $1,152.82
Your company is planning to borrow $500,000 on a 5-year, 8 percent, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal?
A. a. 62.91%
B. b. 45.93%
C. c. 51.32%
D. d. 48.13%
E. e. 73.50%
Which of the following statements is correct?
A. a. Except in situations where compounding occurs annually, the periodic interest rate exceeds the nominal interest rate.
B. b. The effective annual rate always exceeds the nominal rate, no matter how few or many compounding periods occur each year.
C. c. If compounding occurs more frequently than once a year, and if payments are made at times other than at the end of compounding periods, it is impossible to determine present or future values, even with a financial calculator. The reason is that under these conditions, the basic assumptions of discounted cash flow analysis are not met.
D. d. Assume that compounding occurs quarterly, that the nominal interest rate is 8 percent, and that you need to find the present value of $ 1,000 due 6 months from today. You could get the correct answer by discounting the $ 1,000 at 2 percent for 2 periods.
E. e. Statements a, b, c, and d are all false.