Question

You are scheduled to receive annual payments of $4,000 for each of the next 8 years. The discount rate is 8 percent

What is the theoretical relation between the present value if you receive these payments at the beginning of each year and the present value if you receive these payments at the end of each year? (Write the equation)

Answer 1

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Answer:

Present value of ordinary annuity of $ 1 at 8 % for 8 years = [ { 1 - ( 1 / 1.08) ²⁵ } / 0.08 ] = 5.74664

Present value of annuity due of $ 1 at 8 % for 8 years =10.67447619x 1.08 = 6.20637

Present value of ordinary annuity of $ 4,000 = $ 4,000 x5.74664 = $22986.55577

Present value of annuity due of $ 4,000 = $ 4,000 x 6.20637 = $ 24825.48

Difference = $ 24825.48 - 22986.55577 = 1838.924462