(46) What is the future value of a 7%, 5-year ordinary annuity that pays $300 each year?

If this were an annuity due, what would its future value be?

(47)

An investment will pay $100 at the end of each of the next 3 years, $200 at the end of

Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of

equal risk earn 8% annually, what is this investments present value? Its future value?

(8) Annuity Payment and EAR You want to buy a car, and a local bank will lend you $20,000. The loan would be fully amortized over 5 years (60 months), and the nominal interest rate would be 12%, with interest paid monthly. What is the monthly loan payment? What is the loans EFF%?

(49)

Find the following values, using the equations, and then work the problems using a

financial calculator to check your answers. Disregard rounding differences. (Hint:

If you are using a financial calculator, you can enter the known values and then

press the appropriate key to find the unknown variable. Then, without clearing

the TVM register, you can override the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in

many other situations, to see how changes in input variables affect the output

variable.)

a. An initial $500 compounded for 1 year at 6%

b. An initial $500 compounded for 2 years at 6%

c. The present value of $500 due in 1 year at a discount rate of 6%

d. The present value of $500 due in 2 years at a discount rate of 6%

(410)

Use both the TVM equations and a financial calculator to find the following values.

See the Hint for Problem 4-9.

a. An initial $500 compounded for 10 years at 6%

b. An initial $500 compounded for 10 years at 12%

c. The present value of $500 due in 10 years at a 6% discount rate

d. The present value of $500 due in 10 years at a 12% discount rate

(411)

To the closest year, how long will it take $200 to double if it is deposited and

earns the following rates? [Notes: (1) See the Hint for Problem 4-9. (2) This

problem cannot be solved exactly with some financial calculators. For example, if

you enter PV = 200, PMT = 0, FV = 400, and I = 7 in an HP-12C and then

press the N key, you will get 11 years for part a. The correct answer is 10.2448

years, which rounds to 10, but the calculator rounds up. However, the HP-10B

gives the exact answer.]

a. 7%

b. 10%

c. 18%

d. 100%

(412)

Find the future value of the following annuities. The first payment in these annuities

is made at the end of Year 1, so they are ordinary annuities. (Notes: See the Hint to

Problem 4-9. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the annuity due.)

a. $400 per year for 10 years at 10%

b. $200 per year for 5 years at 5%

c. $400 per year for 5 years at 0%

d. Now rework parts a, b, and c assuming that payments are made at the beginning

of each year; that is, they are annuities due.

166 Part 2: Fixed Income Securities

(413)

Find the present value of the following ordinary annuities (see the Notes to Problem 4-12).

a. $400 per year for 10 years at 10%

b. $200 per year for 5 years at 5%

c. $400 per year for 5 years at 0%

d. Now rework parts a, b, and c assuming that payments are made at the beginning

of each year; that is, they are annuities due.

Find the present values of the following cash flow streams. The appropriate interest

rate is 8%. (Hint: It is fairly easy to work this problem dealing with the individual

cash flows. However, if you have a financial calculator, read the section of the manual

that describes how to enter cash flows such as the ones in this problem. This will take

a little time, but the investment will pay huge dividends throughout the course. Note

that, when working with the calculators cash flow register, you must enter CF0 = 0.

Note also that it is quite easy to work the problem with Excel, using procedures described in the Chapter 4 Tool Kit.)

b. What is the value of each cash flow stream at a 0% interest rate?

(415)

Find the interest rate (or rates of return) in each of the following situations.

a. You borrow $700 and promise to pay back $749 at the end of 1 year.

b. You lend $700 and receive a promise to be paid $749 at the end of 1 year.

c. You borrow $85,000 and promise to pay back $201,229 at the end of 10 years.

d. You borrow $9,000 and promise to make payments of $2,684.80 at the end of

each of the next 5 years.

(416)

Find the amount to which $500 will grow under each of the following conditions.

a. 12% compounded annually for 5 years

b. 12% compounded semiannually for 5 years

c. 12% compounded quarterly for 5 years

d. 12% compounded monthly for 5 years

(417)

(418)

Find the future values of the following ordinary annuities.

a. FV of $400 each 6 months for 5 years at a nominal rate of 12%, compounded

semiannually

b. FV of $200 each 3 months for 5 years at a nominal rate of 12%, compounded

Quarterly

The annuities described in parts a and b have the same total amount of money

paid into them during the 5-year period, and both earn interest at the same

nominal rate, yet the annuity in part b earns $101.75 more than the one in part a

over the 5 years. Why does this occur?

(419)

Effective versus Nominal Interest Rates

Universal Bank pays 7% interest, compounded annually, on time deposits. Regional

Bank pays 6% interest, compounded quarterly.

a. Based on effective interest rates, in which bank would you prefer to deposit your

money?

b. Could your choice of banks be influenced by the fact that you might want to

withdraw your funds during the year as opposed to at the end of the year? In

answering this question, assume that funds must be left on deposit during an

entire compounding period in order for you to receive any interest.

(420)

Amortization Schedule

a. Set up an amortization schedule for a $25,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 10%.

b. How large must each annual payment be if the loan is for $50,000? Assume that

the interest rate remains at 10% and that the loan is still paid off over 5 years.

c. How large must each payment be if the loan is for $50,000, the interest rate is

10%, and the loan is paid off in equal installments at the end of each of the next

10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Why are these payments not

half as large as the payments on the loan in part b?