Question

Joe & Moe, both 65, just retired and each received a check from their Retirement Plan. Joe & Moe both have been contributing $ 5,000 each year in their retirement plans since the age of 25. Retirement portfolio of Joe and Moe has been exactly the same with one difference. Joe started contributing at the beginning of each year and Moe at the end of each both year. The average annualized returns both portfolios has been exactly the same, 5% py. Joe is retirement check is greater than Moe’s by:

A. $781

B. $20,983

C. $98,775

D. $5,250

Answer 1

Deposit annual amount		5000
Rate of interest (r ) =		5%
formula for future value of annuity (due in beginning of month)					= P * (1+r)* { (1+r)^n - 1 } / r
formula for future value of annuity (due in End of month)					= P * { (1+r)^n - 1 } / r
Thus, comparing above formula, All amounts and value shall be same. Only difference in two values will be of (1+r). It means who deposit at beginning of month, amount shall be greater than P * (1+r)
So, Joe amount shall be greater than by 5000 * (1+0.05)				5250
Answer is D, $5,250.