Question

Worker A annually invests $1,000 in an IRA for nine years (ages 27 through 35) and never makes another contribution. Worker B annually invests $1,000 in an IRA for thirty years (ages 36 through 65). Which worker will have more in his or her account when he or she retires if they both earn 8 percent on their investments?

Answer 1

Worker A
The formula for the future value of an ordinary annuity, as opposed to an annuity due, is as follows:
P = PMT x ((((1 + r) ^ n) - 1) / r)
Where:
P = the future value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	1000
r = the effective interest rate (also known as the discount rate)	8%
n = the number of periods in which payments will be made	9
Amount at 35th birthday	= PMT x ((((1 + r) ^ n) - 1) / r)
Amount at 35th birthday	= 1000*((((1 + 8%) ^ 9) - 1) / 8%)
Amount at 35th birthday	$ 12,487.56
Now this amount remains invested till his age is 65 so years	30
The amount at 65th birthday=	Investment * (1+rate)^time
The amount at 65th birthday=	12487.56*(1+8%)^30
The amount at 65th birthday=	$125,658.03
Worker B
P = the future value of an annuity stream	To be computed
PMT = the dollar amount of each annuity payment	1000
r = the effective interest rate (also known as the discount rate)	8%
n = the number of periods in which payments will be made	30
Amount at 65th birthday	= PMT x ((((1 + r) ^ n) - 1) / r)
Amount at 65th birthday	= 1000*((((1 + 8%) ^ 30) - 1) / 8%)
Amount at 65th birthday	$113,283.21
As we can see worker A will have more money than worker B.