Question

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

Answer 1

= $ 219,657.43

Step-by-step 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