# TVM Practice

1.  Suppose you are trying to find the present value of two different cash flows.  One is \$100 two periods from now, the other a \$100 flow three periods from now.  Which of the following is/are true about the discount factors used to value the cash flows?

a.  The factor for the flow three periods away is always less than the factor for the flow that is received two periods from now.

b.  The factor for the flow three periods away is always more than the factor for the flow that is received two periods from now.

c.  Whether one factor is larger than the other will depend on the interest rate.

d.  Since the payments are for the same amount, the factors will yield present values that are the same.

e.  None of the above statements are true.

2.    What is the present value of a stream of \$2,500 semiannual payments received at the end of each period for the next 10 years?  The APR is 6%.

a.  37,194

b.  38,310

c.  35,810

d.  36,885

3.  What is the future value in 10 years of \$1,500 payments received at the end of each year for the next 10 years?  Assume an interest rate of 8%.

a.   \$25,260

b.   \$23,470

c.   \$21,730

d.   \$18,395

e.   \$15,000

4.  You are given the option of receiving \$1,000 now or an annuity of \$85 per month for 12 months.  Which of the following is correct?

a.  You cannot choose between the two without computing present values.

b.  You cannot choose between the two without computing future values.

c.  You will always choose the lump sum payment.

d.  You will always choose the annuity.

e.  The choice you would make when comparing the future value of each would be the same as the choice you would make when comparing present values.

5.     You open a savings account that pays 4.5% annually.  How much must you deposit each year in order to have \$50,000 five years from now?

a.   \$8,321

b.   \$9,629

c.   \$8,636

d.   \$9,140

e.   \$6,569

6.  You are considering an investment in a 6-year annuity.  At the end of each year for the next six years you will receive cash flows of \$90.  The initial investment is \$414.30. To the nearest percent, what rate of return are you expecting from this investment? (Annual Compounding)

a.    8%

b.    9%

c.   12%

d.   21%

e.   10%

7.         You are saving up for a down payment on a house. You will deposit \$600 a month for the next 24 months in a money market fund.  How much will you have for your down payment in 24 months if the fund earns 10% APR compounded monthly?

a.   \$14,480

b.   \$15,870

c.   \$12,930

d.   \$10,560

e.   \$  9,890

8.        Your mortgage payment is \$600 per month.  There is exactly 180 payments remaining on the  mortgage.  The interest rate s 8.0%, compounded monthly.  The first payment is due in exactly one month.  What is the balance of the loan?  [Balance = PV of remaining payments.]

a.  \$62,784

b.  \$77,205

c.  \$63,203

d.  \$82,502

e.  \$85,107

9.         Your mortgage payment is \$755 per month.  It is a 30-year mortgage at 9.0% compounded monthly.  How much did you borrow?

a.  \$93,800

b.  \$97,200

c.  \$92,500

d.  \$85,100

e.  \$89,400

10.  What is the value of the following set of cash flows today?   The interest rate is 8.5%.

Year  Cash Flow

0:  -\$1,000      1:    \$ 200        2:    \$ 400        3:    \$ 600      4:    \$ 800

a.   \$ 800

b.   \$ 571

c.   \$1072

d.   \$ 987

e.   \$ 520

11.   The present value interest factor of an annuity due for 3 years at 8% equals:

a.  1/(1.08)3

b.  1/(1.24)

c.  [1 + 1/(1.08) + 1/(1.08)2]

d.  [1/(1.08) + 1/(1.08)2 + 1/(1.08)3]

e.  None of the above.

12.    What is the present value of \$2,500 semiannual payments received at the beginning of each period for the next 10 years?  The APR is 6%.

a.  37,194.70

b.  38,309.50

c.  35,809.50

d.  36,884.80

13.   Your mortgage payment is \$600 per month.  There are exactly 180 payments remaining on the mortgage.  The interest rate s 8.0%, compounded monthly.  The next payment is due immediately.  What is the balance of the loan?  [Hint: This is an annuity due.]

a.  \$63,203

b.  \$77,205

c.  \$62,784

d.  \$82,502

e.  \$85,107

14.   Your mortgage payment is \$600 per month.  There are exactly 180 payments remaining on the mortgage.  The interest rate s 8.0%, compounded monthly.  The next payment is due in 15 days.  What is the balance of the loan?  [Hint: Assume 30 days per month.]

 a \$62,993 b \$76,949 c \$62,576 d \$82,228 e \$84,825

15.   The present value interest factor of an annual ordinary annuity for 3 years at 8% equals:

a.  1/(1.08)3

b.  1/(1.24)

c.  [1 + 1/(1.08) + 1/(1.08)2]

d.  [1/(1.08) + 1/(1.08)2 + 1/(1.08)3]

e.  None of the above.

16.   The present value interest factor of a semiannual ordinary annuity for 3 years at 8% equals:

a   [1/(1.04) + 1/(1.04)2 + 1/(1.04)3]

b.  [1/(1.08) + 1/(1.08)2 + 1/(1.08)3 +1/(1.08)4 + 1/(1.08)5 + 1/(1.08)6]

c.  [1/(1.04) + 1/(1.04)2 + 1/(1.04)3 + 1/(1.04)4 + 1/(1.04)5 + 1/(1.04)6]

d.  [1/(1.08) + 1/(1.08)2 + 1/(1.08)3]

e.  None of the above.

17.   The future value interest factor of an ordinary annuity for 3 years at 8% equals:

a.  (1.08)3

b.  (1.24)

c.  [1 + (1.08) + 1.08)2]

d.  [(1.08) + (1.08)2 + (1.08)3]

e.  None of the above.

18.    Suppose an annuity costs \$40,000 and produces cash flows of \$10,000 over each of the following eight years.  What is the rate of return on the annuity?

a.   0%

b.   10.5%

c.   18.6%

d.   25.0%

e. 50.0%