14 Suppose you just bought an annuity with 25 annual payments of $7.900 per year

Question

14 Suppose you just bought an annuity with 25 annual payments of $7.900 per year at the current interest rate of 12 percent per year. 9 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 7 a. eBook b. 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 17 percent? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) a. Annual deposit at 12 percent b. Annual deposit at 7 percent c. Annual deposit at 17 percent

Explanation / Answer

Answer a We can use the present value of annuity formula to calculate the annuity's today's value. Present value of annuity = P x {[1 - (1+r)^-n]/r} Present value of annuity = value of annuity today = ? P = annual payments = $7900 r = rate of interest per annum = 12% n = no.of annual payments = 25 Present value of annuity = 7900 x {[1 - (1+0.12)^-25]/0.12} Present value of annuity = 7900 x 7.843139 Present Value of annuity = 61960.80 Value of your annuity today = $61,960.80 Answer b We can use the present value of annuity formula to calculate the annuity's today's value. Present value of annuity = P x {[1 - (1+r)^-n]/r} Present value of annuity = value of annuity today = ? P = annual payments = $7900 r = rate of interest per annum = 7% n = no.of annual payments = 25 Present value of annuity = 7900 x {[1 - (1+0.07)^-25]/0.07} Present value of annuity = 7900 x 11.65358 Present Value of annuity = 92,063.31 Value of your annuity today = $92,063.31 Answer c We can use the present value of annuity formula to calculate the annuity's today's value. Present value of annuity = P x {[1 - (1+r)^-n]/r} Present value of annuity = value of annuity today = ? P = annual payments = $7900 r = rate of interest per annum = 17% n = no.of annual payments = 25 Present value of annuity = 7900 x {[1 - (1+0.17)^-25]/0.17} Present value of annuity = 7900 x 5.766234 Present Value of annuity = 45,553.25 Value of your annuity today = $45,553.25

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