rue/False

Indicate whether the statement is true or false.

____1.If the discount (or interest) rate is positive, the present value of an expected series of payments will always exceed the future value of the same series.

____2.Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.

____3.If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual rate.

____4.The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the greater the percentage of the payment that will be a repayment of principal.

____5.The greater the number of compounding periods within a year, then (1) the greater the future value of a lump sum investment at Time 0 and (2) the greater the present value of a given lump sum to be received at some future date.

____6.Suppose an investor plans to invest a given sum of money. She can earn an effective annual rate of 5% on Security A, while Security B will provide an effective annual rate of 12%. Within 11 years' time, the compounded value of Security B will be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding occurs daily.)

____7.The present value of a future sum decreases as either the discount rate or the number of periods per year increases.

Multiple Choice

Identify the choice that best completes the statement or answers the question.

____8.Which of the following bank accounts has the highest effective annual return?

a.

An account that pays 8% nominal interest with monthly compounding.

b.

An account that pays 8% nominal interest with annual compounding.

c.

An account that pays 7% nominal interest with daily (365-day) compounding.

d.

An account that pays 7% nominal interest with monthly compounding.

e.

An account that pays 8% nominal interest with daily (365-day) compounding.

____9.Your bank account pays a 6% nominal rate of interest. The interest is compounded quarterly. Which of the following statements is CORRECT?

a.

The periodic rate of interest is 1.5% and the effective rate of interest is 3%.

b.

The periodic rate of interest is 6% and the effective rate of interest is greater than 6%.

c.

The periodic rate of interest is 1.5% and the effective rate of interest is greater than 6%.

d.

The periodic rate of interest is 3% and the effective rate of interest is 6%.

e.

The periodic rate of interest is 6% and the effective rate of interest is also 6%.

____10.Which of the following statements is NOT CORRECT?

a.

The present value of a 3-year, $150 annuity due will exceed the present value of a 3-year, $150 ordinary annuity.

b.

If a loan has a nominal annual rate of 8%, then the effective rate can never be less than 8%.

c.

If a loan or investment has annual payments, then the effective, periodic, and nominal rates of interest will all be the same.

d.

The proportion of the payment that goes toward interest on a fully amortized loan declines over time.

e.

An investment that has a nominal rate of 6% with semiannual payments will have an effective rate that is less than 6%.

____11.Last year Toto Corporation's sales were $225 million. If sales grow at 6% per year, how large (in millions) will they be 5 years later?

a.

$271.74

b.

$286.05

c.

$301.10

d.

$316.16

e.

$331.96

____12.You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?

a.

$2,245.08

b.

$2,363.24

c.

$2,481.41

d.

$2,605.48

e.

$2,735.75

____13.Suppose a U.S. government bond promises to pay $1,000 five years from now. If the going interest rate on 5-year government bonds is 5.5%, how much is the bond worth today?

a.

$765.13

b.

$803.39

c.

$843.56

d.

$885.74

e.

$930.03

____14.How much would $5,000 due in 50 years be worth today if the discount rate were 7.5%?

a.

$109.51

b.

$115.27

c.

$121.34

d.

$127.72

e.

$134.45

____15.Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

a.

4.37%

b.

4.86%

c.

5.40%

d.

6.00%

e.

6.60%

____16.Ten years ago, Levin Inc. earned $0.50 per share. Its earnings this year were $2.20. What was the growth rate in Levin's earnings per share (EPS) over the 10-year period?

a.

15.17%

b.

15.97%

c.

16.77%

d.

17.61%

e.

18.49%

____17.How many years would it take $50 to triple if it were invested in a bank that pays 3.8% per year?

a.

23.99

b.

25.26

c.

26.58

d.

27.98

e.

29.46

____18.You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning one year from today. You will deposit your savings in an account that pays 5.2% interest. How much will you have just after you make the 3rd deposit, 3 years from now?

a.

$11,973.07

b.

$12,603.23

c.

$13,266.56

d.

$13,929.88

e.

$14,626.38

____19.You want to buy a new sports car 3 years from now, and you plan to save $4,200 per year, beginning immediately. You will make 3 deposits in an account that pays 5.2% interest. Under these assumptions, how much will you have 3 years from today?

a.

$13,956.42

b.

$14,654.24

c.

$15,386.95

d.

$16,156.30

e.

$16,964.11

____20.What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 6.5%?

a.

$15,809.44

b.

$16,641.51

c.

$17,517.38

d.

$18,439.35

e.

$19,409.84

____21.Your aunt is about to retire, and she wants to buy an annuity that will supplement her income by $65,000 per year for 25 years, beginning a year from today. The going rate on such annuities is 6.25%. How much would it cost her to buy such an annuity today?

a.

$770,963.15

b.

$811,540.16

c.

$852,117.17

d.

$894,723.02

e.

$939,459.18

____22.What is the PV of an annuity due with 10 payments of $2,700 at an interest rate of 6.5%?

a.

$20,671.48

b.

$21,705.06

c.

$22,790.31

d.

$23,929.82

e.

$25,126.31

____23.You have a chance to buy an annuity that pays $550 at the beginning of each year for 3 years. You could earn 5.5% on your money in other investments with equal risk. What is the most you should pay for the annuity?

a.

$1,412.84

b.

$1,487.20

c.

$1,565.48

d.

$1,643.75

e.

$1,725.94

____24.What's the present value of a 4-year ordinary annuity of $2,250 per year plus an additional $3,000 at the end of Year 4 if the interest rate is 5%?

a.

$8,508.74

b.

$8,956.56

c.

$9,427.96

d.

$9,924.17

e.

$10,446.50

____25.Your uncle has $375,000 and wants to retire. He expects to live for another 25 years, and he also expects to earn 7.5% on his invested funds. How much could he withdraw at the beginning of each of the next 25 years and end up with zero in the account?

a.

$28,243.21

b.

$29,729.70

c.

$31,294.42

d.

$32,859.14

e.

$34,502.10

____26.Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years?

a.

$22,598.63

b.

$23,788.03

c.

$25,040.03

d.

$26,357.92

e.

$27,675.82

____27.Your uncle has $375,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. How many years will it take to exhaust his funds, i.e., run the account down to zero?

a.

22.50

b.

23.63

c.

24.81

d.

26.05

e.

27.35

____28.You just won the state lottery, and you have a choice between receiving $3,500,000 today or a 10-year annuity of $500,000, with the first payment coming one year from today. What rate of return is built into the annuity?

a.

6.72%

b.

7.07%

c.

7.43%

d.

7.80%

e.

8.19%

____29.Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. Your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?

a.

6.85%

b.

7.21%

c.

7.59%

d.

7.99%

e.

8.41%

____30.What's the present value of a perpetuity that pays $250 per year if the appropriate interest rate is 5%?

a.

$4,750.00

b.

$5,000.00

c.

$5,250.00

d.

$5,512.50

e.

$5,788.13

____31.At a rate of 6.25%, what is the present value of the following cash flow stream? $0 at Time 0; $75 at the end of Year 1; $225 at the end of Year 2; $0 at the end of Year 3; and $300 at the end of Year 4?

a.

$411.57

b.

$433.23

c.

$456.03

d.

$480.03

e.

$505.30

____32.What is the present value of the following cash flow stream at an interest rate of 12.0% per year? $0 at Time 0; $1,500 at the end of Year 1; $3,000 at the end of Year 2; $4,500 at the end of Year 3; and $6,000 at the end of Year 4.

a.

$9,699.16

b.

$10,209.64

c.

$10,746.99

d.

$11,284.34

e.

$11,848.55

____33.An investment promises the following cash flow stream: $750 at Time 0; $2,450 at the end of Year 1 (or at t = 1); $3,175 at the end of Year 2; and $4,400 at the end of Year 3. At a discount rate of 8.0%, what is the present value of the cash flow stream?

a.

$7,916.51

b.

$8,333.17

c.

$8,771.76

d.

$9,233.43

e.

$9,695.10

____34.What is the present value of the following cash flow stream if the interest rate is 6.0% per year? 0 at Time 0; $1,000 at the end of Year 1; and $2,000 at the end of Years 2, 3, and 4.

a.

$5,986.81

b.

$6,286.16

c.

$6,600.46

d.

$6,930.49

e.

$7,277.01

____35.What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?

a.

$1,819.33

b.

$1,915.08

c.

$2,015.87

d.

$2,116.67

e.

$2,222.50

____36.Your uncle has $300,000 invested at 7.5%, and he now wants to retire. He wants to withdraw $35,000 at the end of each year, beginning at the end of this year. He also wants to have $25,000 left to give you when he ceases to withdraw funds from the account. For how many years can he make the $35,000 withdrawals and still have $25,000 left in the end?

a.

14.21

b.

14.96

c.

15.71

d.

16.49

e.

17.32

____37.You agree to make 24 deposits of $500 at the beginning of each month into a bank account. At the end of the 24th month, you will have $13,000 in your account. If the bank compounds interest monthly, what nominal annual interest rate will you be earning?

a.

7.62%

b.

8.00%

c.

8.40%

d.

8.82%

e.

9.26%

____38.At a rate of 6.5%, what is the future value of the following cash flow stream? $0 at Time 0; $75 at the end of Year 1; $225 at the end of Year 2; $0 at the end of Year 3; and $300 at the end of Year 4?

a.

$526.01

b.

$553.69

c.

$582.83

d.

$613.51

e.

$645.80

____39.What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded monthly?

a.

$1,922.11

b.

$2,023.28

c.

$2,124.44

d.

$2,230.66

e.

$2,342.19

____40.If a bank pays a 4.50% nominal rate, with monthly compounding on deposits, what effective annual rate (EFF%) does the bank pay?

a.

3.01%

b.

3.35%

c.

3.72%

d.

4.13%

e.

4.59%

____41.Suppose your credit card issuer states that it charges a 15.00% nominal annual rate. If you must make monthly payments, which amounts to monthly compounding, what is the effective annual rate?

a.

15.27%

b.

16.08%

c.

16.88%

d.

17.72%

e.

18.61%

____42.Pace Co. borrowed $25,000 at a rate of 7.25%, simple interest, with interest paid at the end of each month. The bank uses a 360-day year. How much interest would Pace have to pay in a 30-day month?

a.

$136.32

b.

$143.49

c.

$151.04

d.

$158.59

e.

$166.52

____43.Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. How large would your payments be?

a.

$3,704.02

b.

$3,889.23

c.

$4,083.69

d.

$4,287.87

e.

$4,502.26

____44.Suppose you are buying your first house for $210,000, and are making a $20,000 down payment. You have arranged to finance the remaining amount with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate. What will your equal monthly payments be?

a.

$1,083.84

b.

$1,140.88

c.

$1,200.93

d.

$1,260.98

e.

$1,324.02

____45.Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. How much interest would you have to pay in the first year?

a.

$925.97

b.

$974.70

c.

$1,026.00

d.

$1,080.00

e.

$1,134.00

____46.You plan to borrow $30,000 at a 7% annual interest rate. The terms require you to amortize the loan with 6 equal end-of-year payments. How much interest would you be paying in Year 2?

a.

$1,548.79

b.

$1,630.30

c.

$1,716.11

d.

$1,806.43

e.

$1,896.75

____47.You plan to borrow $75,000 at a 7% annual interest rate. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?

a.

$4,395.19

b.

$4,626.52

c.

$4,870.02

d.

$5,113.52

e.

$5,369.19

____48.You are considering investing in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months will it take for your account to grow to $250,000? Round fractional years up.

a.

23

b.

27

c.

32

d.

38

e.

44

____49.You just deposited $2,500 in a bank account that pays a 12% nominal interest rate, compounded quarterly. If you also add another $5,000 to the account one year (12 months) from now and another $7,500 to the account two years from now, how much will be in the account three years (12 quarters) from now?

a.

$17,422.59

b.

$18,339.57

c.

$19,256.55

d.

$20,219.37

e.

$21,230.34

____50.Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. By how much would you reduce the amount you owe in the first year?

a.

$2,492.82

b.

$2,624.02

c.

$2,755.23

d.

$2,892.99

e.

$3,037.64

____51.Suppose you borrowed $12,000 at a rate of 9% and must repay it in 4 equal installments at the end of each of the next 4 years. How much would you still owe at the end of the first year, after you have made the first payment?

a.

$7,636.79

b.

$8,038.73

c.

$8,461.82

d.

$8,907.18

e.

$9,375.98