The relationship between the value of an annuity and the level of interest rates

Question

The relationship between the value of an annuity and the level of interest rates is as follows: The present value of an annuity  as r rises; the future value of an annuity  as r rises. Suppose you just bought a 7-year annuity of $8,000 per year at the current interest rate of 9 percent per year. The present value of this investment is $. If interest rates suddenly rise to 14 percent, the present value of your investment  to $. If, instead, interest rates suddenly drop to 4 percent, the present value of your investment  to $. (Do not include the dollar sign ($). Round your answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

present value of this investment = 8000/1.09 + 8000/1.09^2 + 8000/1.09^3 + 8000/1.09^4 + 8000/1.09^5 +8000/1.09^6 + 8000/1.09^7 =$40,263.62

If interest rates suddenly rise to 14 percent, the present value of your investment = 8000/1.14 + 8000/1.14^2 + 8000/1.14^3 + 8000/1.14^4 + 8000/1.14^5 +8000/1.14^6 + 8000/1.14^7 =$34,306.44

interest rates suddenly drop to 4 percent, the present value of your investment = 8000/1.04 + 8000/1.04^2 + 8000/1.04^3 + 8000/1.04^4 + 8000/1.04^5 +8000/1.04^6 + 8000/1.04^7 =$48,016.44

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