Question

Suppose you just bought an annuity with 11 annual payments of $8,500 per year at the current interest rate of 10 percent per year.

a.	What is the value of your annuity today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.	What happens to the value of your investment if interest rates suddenly drop to 5 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.	What if interest rates suddenly rise to 15 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Answer a.

Annual Payment = $8,500
Interest Rate = 10%
Period of Annuity = 11 years

Present Value = $8,500/1.10 + $8,500/1.10^2 + ... + $8,500/1.10^10 + $8,500/1.10^11
Present Value = $8,500 * (1 - (1/1.10)^11) / 0.10
Present Value = $8,500 * 6.495061
Present Value = $55,208.02

Answer b.

Annual Payment = $8,500
Interest Rate = 5%
Period of Annuity = 11 years

Present Value = $8,500/1.05 + $8,500/1.05^2 + ... + $8,500/1.05^10 + $8,500/1.05^11
Present Value = $8,500 * (1 - (1/1.05)^11) / 0.05
Present Value = $8,500 * 8.306414
Present Value = $70,604.52

Answer c.

Annual Payment = $8,500
Interest Rate = 15%
Period of Annuity = 11 years

Present Value = $8,500/1.15 + $8,500/1.15^2 + ... + $8,500/1.15^10 + $8,500/1.15^11
Present Value = $8,500 * (1 - (1/1.15)^11) / 0.15
Present Value = $8,500 * 5.233712
Present Value = $44,486.55