Question

Colin is trying to decide whether he should make his IRA contribution at the beginning of the year or at the end of the year. He wants to save $5,000 per year for 25 years in his IRA that can earn 8% per year. What would be the difference in his account value if he made the payments at the beginning of each year rather than at the end?

		$338,382.
		$22,137.
		$29,242.
		$394,772.

Answer 1

Ans $ 29242

P =	Periodic payments
r =	rate of interest
n =	no of years
IF PAYMENT MADE AFTER THE END OF THE YEAR
Future Value of Annuity =	P ( (1 + r)n - 1 ) / r
	5000* ((1 + 8%)^25 - 1) / (8%)
	$ 365530
IF PAYMENT MADE AT THE BEGINNING OF THE YEAR
Future Value of Annuity Due =	(1 + r) * P ( (1 + r)n - 1 ) / r
	(1 + 8%) * 5000* ((1 + 8%)^25 - 1) / (8%)
	$ 394772
DIFFERENCE OF FUTURE VALUE =	394772 - 365530
	$ 29242