You are scheduled to receive annual payments of $60,000 for each of the next 20 years. The annual rate of return is 8 percent. What is the difference in the future value in year 20 if you receive these payments at the beginning of each year rather than at the end of each year

= $ 219,657.43

Explanation:

FV of annuity = P x [(1+r) n -1/r]

P = Periodic payment = $ 20,000

r = Periodic interest rate = 0.08

n = Number of periods = 20

FV = $ 60,000 x [(1+ 0.08)20 -1/0.08]

  = $ 60,000 x [(1.08)20 -1/0.08]

  = $ 60,000 x [(4.66095714384931 -1)/0.08]

  = $ 60,000 x (3.66095714384931/0.08)

= $ 60,000 x 45.7619642981163

= $ 2,745,717.85788698 or $ 2,745,717.86

FV of annuity due =(1+r) x P x [(1+r) n -1/r]

                              = (1+0.08) x $ 2,745,717.85788698

                              = 1.08 x $ 2,745,717.85788698

                             = $ 2,965,375.28651794 or $ 2,965,375.29

Difference in FV of ordinary annuity and annuity due

                             = $ 2,965,375.29 - $ 2,745,717.86

                             = $ 219,657.43

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