Suppose you are going to receive $12,500 per year for six years. The appropriate

Question

Suppose you are going to receive $12,500 per year for six years. The appropriate interest rate is 7.4 percent What is the present value of the payments if they are in the form of an ordinary annuity? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g,32.16.) Present value What is the present value if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) Present value Suppose you plan to invest these payments. How much will you have in six years if the payments are an ordinary annuilty? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g, 32.16.) Future value Suppose you plan to invest these annual payments. How much will you have in six years if the payments are an annuity due? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g-32.16.) Future value References eBook &Resources; Worksheet Type here to search

Explanation / Answer

Calculation of present value of ordinary annuity Present value of annuity = P * {[1 - (1+r)^-n]/r} P = Yearly payment = $12500 r = rate of interest per year = 7.4% n = no.of years = 6 Present value of annuity = 12500 * {[1 - (1+0.074)^-6]/0.074} Present value of annuity = 12500 * 4.708245 Present value of annuity = $58,853.07 Calculation of present value of annuity due Present value of annuity due = P + P * {[1 - (1+r)^-(n-1)]/r} P = Yearly payment = $12500 r = rate of interest per year = 7.4% n = no.of years = 6 Present value of annuity due = 12500 + 12500 * {[1 - (1+0.074)^-(6-1)]/0.074} Present value of annuity due = 12500 + 12500 * 4.056655 Present value of annuity due = $63,208.19 Calculation of Future value of ordinary annuity Future value of annuity = P * {[(1+r)^n - 1]/r} P = Yearly payment = $12500 r = rate of interest per year = 7.4% n = no.of years = 6 Future value of annuity = 12500 * {[(1+0.074)^6 - 1]/0.074} Future value of annuity = 12500 * 7.22578 Future value of annuity = $90,322.26 Calculation of Future value of annuity due Future value of annuity due = (1+r) * P{[(1+r)^n - 1]/r} P = Yearly payment = $12500 r = rate of interest per year = 7.4% n = no.of years = 6 Future value of annuity due = (1+0.074) * 12500 {[(1+0.074)^6 - 1]/0.074} Future value of annuity due = 1.074 * 90322.26 Future value of annuity due = $97,006.10

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