Question

Retirement planning  Personal Finance Problem   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 11​% over the next 35 years.

a.  If Hal makes​ end-of-year ​$2,200 deposits into the​ IRA, how much will he have accumulated in 35 years when he turns 60​?

b.  If Hal decides to wait until age 35 to begin making​ end-of-year ​$2,200 deposits into the​ IRA, how much will he have accumulated when he retires 25 years​ later?

c.  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 60th 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 60th year.

Answer 1

a)

The futire value of deposits is found using the following equation

The amount accumulated in 35 years = $ 751497.02

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b)

If deposits are started at the age of 35.

The amount accumulated in 25 years = $ 251,709.28

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c)

Difference in the total amount accumulated by delaying the deposits = $ 751497.02 -  $ 251,709.28 = $ 499787.74

By delaying the deposits into the account for 10 years, the account will have a shortage of $ 499787.74 .

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d)

If the deposits are made at the beginning, the future value of deposits is found using the following equation

If deposit is started at the age of 25 years,

The amount accumulated in 35 years = $ 834,161.69

By depositing at the beginning of the year, the account will have an excess of $ 82664.67

If deposit is started at the age of 35 years

FV at the end of 60 years = $ 279,397.30

By depositing at the beginning of the year, the account will have an excess of $ 27688.02

Difference due to delaying = $ 834,161.69 -  $ 279,397.30 = $ 554,764.39

By delaying the deposits by 10 years, the account will have a shortage of $ 554,764.39 , even if the deposits are made at the beginning of each year.