Question

a. An initial $500 compounded for 10 years at 8%.

b. An initial $500 compounded for 10 years at 16%.

c. The present value of $500 due in 10 years at 8%.

d. The present value of $2,325 due in 10 years at 16% and at 8%.

e. Define present value. (choose one of the following)

1. The present value is the value today of a sum of money to be received in the future and in general is less than the future value.
2. The present value is the value today of a sum of money to be received in the future and in general is greater than the future value.
3. The present value is the value today of a sum of money to be received in the future and in general is equal to the future value.
4. The present value is the value in the future of a sum of money to be received today and in general is less than the future value.
5. The present value is the value in the future of a sum of money to be received today and in general is greater than the future value.

f. How are present values affected by interest rates? (choose one of the following)

1. Assuming positive interest rates, the present value will increase as the interest rate increases.
2. Assuming positive interest rates, the present value will decrease as the interest rate increases.
3. Assuming positive interest rates, the present value will decrease as the interest rate decreases.
4. Assuming positive interest rates, the present value will not change as the interest rate increases.
5. Assuming positive interest rates, the present value will not change as the interest rate decreases.

Answer 1

a]

Future value = present value * (1 + r)ⁿ,

where r = interest rate per period,

and n = number of periods.

Here, the r = annual interest rate, which is 8%

n = number of years, which is 10.

Future value = $500 * (1 + 8%)¹⁰

Future value = $1,079.46

b]

Future value = present value * (1 + r)ⁿ,

where r = interest rate per period,

and n = number of periods.

Here, the r = annual interest rate, which is 16%

n = number of years, which is 10.

Future value = $500 * (1 + 16%)¹⁰

Future value = $2,205.72

c]

Present value = future value / (1 + r)ⁿ,

where r = interest rate per period,

and n = number of periods.

Here, the r = annual interest rate, which is 8%

n = number of years, which is 10.

Present value = $500 / (1 + 8%)¹⁰

Future value = $231.60

d]

16%

Present value = future value / (1 + r)ⁿ,

where r = interest rate per period,

and n = number of periods.

Here, the r = annual interest rate, which is 16%

n = number of years, which is 10.

Present value = $2,325 / (1 + 16%)¹⁰

Future value = $527.04

8%

Present value = future value / (1 + r)ⁿ,

where r = interest rate per period,

and n = number of periods.

Here, the r = annual interest rate, which is 8%

n = number of years, which is 10.

Present value = $2,325 / (1 + 8%)¹⁰

Future value = $1,076.92