Question

A.Calculate the present value of an annuity of $5,000 received annually that begins today and continues for 10 years, assuming a discount rate of 9%.

B. Joan invested $5,000 in an interest-bearing account earning an 8% annual rate of interest compounded monthly. How much will the account be worth at the end of 5 years, assuming all interest is reinvested at the 8% rate?

C. Calculate the present value of an ordinary annuity of $5,000 received annually for 10 years, assuming a discount rate of 9%.

D. Calculate the future value of $10,000 invested for 10 years, assuming an annual interest rate of 9%.

E. Calculate the present value of $10,000 to be received in exactly 10 years, assuming an annual interest rate of 9%.

Answer 1

Answer A.

Annual Payment at the beginning of each year = $5,000
Period = 10 years
Interest Rate = 9%

Present Value = $5,000 + $5,000/1.09 + $5,000/1.09^2 + ... + $5,000/1.09^9
Present Value = $5,000 * 1.09 * (1 - (1/1.09)^10) / 0.09
Present Value = $5,000 * 6.9952
Present Value = $29,976

Answer B.

Amount Invested = $5,000
Annual Interest Rate = 8%
Monthly Interest Rate = 8%/12 = 0.667%
Period = 5 years or 60 months

Accumulated Sum = $5,000 * 1.00667^60
Accumulated Sum = $5,000 * 1.4901
Accumulated Sum = $7,451

Answer C.

Annual Payment = $5,000
Period = 10 years
Interest Rate = 9%

Present Value = $5,000/1.09 + $5,000/1.09^2 + ... + $5,000/1.09^10
Present Value = $5,000 * (1 - (1/1.09)^10) / 0.09
Present Value = $5,000 * 6.4177
Present Value = $32,089