Question

Retirement planning Hal Thomas, a 25-year-old college graduate, wishes to retire at age 65. To supplement other sources of retirement income, he can deposit $2,000 each year into a tax-deferred individual retirement arrangement (IRA). The IRA will earn a 10% return over the next 40 years.

1. If Hal makes end-of-year $2,000 deposits into the IRA, how much will he have accumulated in 40 years when he turns 65?

2. If Hal decides to wait until age 35 to begin making end-of-year $2,000 deposits into the IRA, how much will he have accumulated when he retires 30 years later?

3. Using your findings in parts a and b, discuss the impact of delaying deposits into the IRA for 10 years (age 25 to age 35) on the amount accumulated by the end of Hal’s sixty-fifth year.

4. Rework parts a, b, and c, assuming that Hal makes all deposits at the beginning, rather than end, of each year. Discuss the effect of beginning-of-year deposits on the future value accumulated by the end of Hal’s sixty-fifth year.

Answer 1

a)

Future value = Annuity * [(1 + r)ⁿ - 1] / r

Future value = 2000 * [(1 + 0.1)⁴⁰ - 1] / 0.1

Future value = 2000 * 442.592556

Future value = $885,185.11

$885,185.11 will be accumulated in 40 years

b)

Future value = Annuity * [(1 + r)ⁿ - 1] / r

Future value = 2000 * [(1 + 0.1)³⁰ - 1] / 0.1

Future value = 2000 * 164.494023

Future value = $328,988.05

$328,988.05 will be accumulated in 30 years

c)

Difference = 885,185.11 - 328,988.05 = 556,197.06

As you can see, a delay in payments will lead to a significantly lower future value. As more time is given, interest is earned on interest. This makes investments to have a significantly higher future value. The early you start, the better it is.

d)

Future value of annuity due = (1 + r) * Annuity * [(1 + r)ⁿ - 1] / r

Future value of annuity due = (1 + 0.1) * 2000 * [(1 + 0.1)⁴⁰ - 1] / 0.1

Future value of annuity due = 1.1 * 2000 * 442.592556

Future value of annuity due = $973,703.62

$973,703.62 will be accumulated in 40 years

Future value of annuity due = (1 + r) *Annuity * [(1 + r)ⁿ - 1] / r

Future value of annuity due = (1 + 0.1) * 2000 * [(1 + 0.1)³⁰ - 1] / 0.1

Future value of annuity due = (1.1) * 2000 * 164.494023

Future value of annuity due = $361,886.85

$361,886.85 will be accumulated in 30 years

Difference = 973,703.62 - 361,886.85 = 611,816.77

The future value of annuity dues will be higher than the future values of ordinary annuities.This is because there is an extra period in annuity due since payments are paid at the beginning of the periods. As you can see, a delay in payments will lead to a significantly lower future value. As more time is given, interest is earned on interest. This makes investments to have a significantly higher future value. The early you start, the better it is.