Retirement planning Personal Finance Problem Hal Thomas, a $30-$year$-$old college graduate, wishes to retire at age $65.$ To supplement other sources of retirement income, he can deposit

$$2,300$ 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 $$2,300$ deposits into the IRA, how much will he have accumulated in $35$ years when he turns $65?$

b$.$ If Hal decides to wait until age $40$ to begin making end$-$of$-$year $$2,300$ 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 $30$ to age $40)$ on the amount accumulated by the end of Hal's $65$ th 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 $65$th year.

a$.$ If Hal makes annual end$-$of$-$year $$2,300$ deposits into the IRA, the amount he will have accumulated by the end of his $65$ th year is $

$($Round to the nearest cent.$)$

b$.$ If Hal decides to wait until age $40$ to begin making annual end$-$of$-$year $$2,300$ deposits into the IRA, the amount he will have accumulated by the end of his $65$ th year is $

nearest cent.$)$

c$.$ Using your findings in parts a and $b,$ which of the following options better describes the impact of delaying making deposits into the IRA for $10$ years $($age $30$ to age $40)$ on the amount

accumulated by the end of Hal's $65$th year? $($Select the best answer below.$)$

By delaying the deposits by $10$ years, Hal is incurring a significant opportunity cost. This cost is due to both the lost deposits of $$23,000($ $$2,30010$ yrs$.)$ and the lost compounding of interest

on all of the money for $10$ years.

By delaying the deposits by $10$ years, Hal earns a large capital gain. This gain is due to both the saved deposits of yrs$.)$ and the gained compounding of interest on all

of the money not deposited for $10$ years.

d$.$ If Hal makes annual beginning$-$of$-$year $$2,300$ deposits into the IRA, the amount he will have accumulated by the end of his $65$ th year is $ $($Round to the nearest cent.$)$

If Hal decides to wait until age $40$ to begin making annual beginning$-$of$-$year $$2,300$ deposits into the IRA, the amount he will have accumulated by the end of $$65$ th year is $

$($Round to the

nearest cent.$)$

Both deposits $($increased$/$decreased$)$ due to the extra year of compounding from the beginning$-$of$-$year deposits instead of the end$-$of$-$year deposits. The incremental change in the $(35-$year$/25-$year$)$ annuity is much

larger than the incremental compounding on the $(35-$year$/25-$year$)$

deposit due to the larger sum on which the last year of compounding occurs.