Suppose you just bought an annuity with 15 annual payments of $8,000 per year at

Question

Suppose you just bought an annuity with 15 annual payments of $8,000 per year at the current interest rate of 11 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.) What happens to the value of your investment if interest rates suddenly drop to 6 decimal places, e.g., 32.16.) calculations and round your answer to 2 decimal places, e.g., 32.16.) b. percent? (Do not round intermediate calculations and round your answer to 2 c. What if interest rates suddenly rise to 16 percent? (Do not round intermediate a. Annual deposit at 11 percent b. Annual deposit at 6 percent c. Annual deposit at 16 percent

Explanation / Answer

Answer a.

Annual Payment = $8,000
Period = 15 years
Interest Rate = 11%

Present Value = $8,000/1.11 + $8,000/1.11^2 + $8,000/1.11^3 + ... + $8,000/1.11^15
Present Value = $8,000 * (1 - (1/1.11)^15) / 0.11
Present Value = $8,000 * 7.19087
Present Value = $57,526.96

Answer b.

Annual Payment = $8,000
Period = 15 years
Interest Rate = 6%

Present Value = $8,000/1.06 + $8,000/1.06^2 + $8,000/1.06^3 + ... + $8,000/1.06^15
Present Value = $8,000 * (1 - (1/1.06)^15) / 0.06
Present Value = $8,000 * 9.71225
Present Value = $77,698.00

Answer c.

Annual Payment = $8,000
Period = 15 years
Interest Rate = 16%

Present Value = $8,000/1.16 + $8,000/1.16^2 + $8,000/1.16^3 + ... + $8,000/1.16^15
Present Value = $8,000 * (1 - (1/1.16)^15) / 0.16
Present Value = $8,000 * 5.57546
Present Value = $44,603.68

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