Question

Hal​ Thomas, a 25​-year-old college​ graduate, wishes to retire at age 60. To supplement other sources of retirement​ income, he can deposit 2,200 each year into a​ tax-deferred individual retirement arrangement​ (IRA). The IRA will earn a return of 12​% over the next 35 years.

a.  If Hal makes annual​ end-of-year ​$2,200 deposits into the​ IRA, how much will he have accumulated by the end of his 60th ​year?

b.  If Hal decides to wait until age 35 to begin making annual​ $2,200 deposits into the​ IRA, how much will he have accumulated by the end of his 60th ​year?

c.  Using your findings in parts a and ​b, discuss the impact of delaying making deposits into the IRA for 10 years​ (age 25 to age 35​) on the amount accumulated by the end of​ Hal's 60th year.

d.  Rework parts a and b 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 60th year.

Answer 1

The tax deferred arrangement is similar to an ordiany annuity. The future value of an ordinary annuity is computed as follows -

where, FV = future value, Amount = equal amount deposited, r = rate of interest, n = number of periods (years)

a) Amount = $2200, r = 12%, n =35

or $949,659.69

b) Amount = $2200, r = 12%, n = 25

or $293,334.51

c) Less payment received / impact = $949659.69 - $293334.51 = $656,325.18

d) In case payments are made at the beginning of a year/ period, it amounts to an annuity due. The future value of an annuity due is computed as follows -

Notice that since the payments are made at the beginning of a year, each amount will remain in invested for 1 more extra year.

In case he invests when he is 25 years old -

or $1,063,618.86

In case he invests when he is 35 years old -

or $328,534.66

Hal would have slightly more amounts in this case as the amounts stay invested for 1 more period!