Question

Retirement planning  

   Hal​ Thomas, a 35​-year-old college​ graduate, wishes to retire at age 65. To supplement other sources of retirement​ income, he can deposit ​$2,100 each year into a​ tax-deferred individual retirement arrangement​ (IRA). The IRA will earn a return of 14​% over the next 30 years.

a.  If Hal makes​ end-of-year ​$2,100 deposits into the​ IRA, how much will he have accumulated in 30 years when he turns 65​?

b.  If Hal decides to wait until age 45 to begin making​ end-of-year ​$2,100 deposits into the​ IRA, how much will he have accumulated when he retires 20 years​ later?

c.  Using your findings in parts a and ​b, discuss the impact of delaying deposits into the IRA for 10 years​ (age 35 to age 45​) on the amount accumulated by the end of​ Hal's 65th

year.

d.  Rework parts ​a, b, and c assuming that Hal makes all deposits at the​ beginning, rather than the​ end, of each year. Discuss the effect of​ beginning-of-year deposits on the future value accumulated by the end of​ Hal's 65th year.

Answer 1

a	Amount at age of 65	$749,252.38
b	Amount at age of 65	$191,152.35

c: The amount accumulated in 20 years is not proportionate to the change in term. It is much lesser due to the loss of interest on the compounded amount.

d	Amount at age of 65	$854,147.71
	Amount at age of 65	$217,913.68

The amounts increase substantially due to beginning of year deposits. This is due to benefits of faster compounding.

Workings