Retirement planning Personal Finance Problem Hal Thomas, a $25-$year$-$old college graduate, wishes to retire at age $65.$ To supplement other sources of retirement income, he can deposit $$2,200$ each year into a tax$-$deferred individual retirement arrangement $($IRA$).$ The IRA will earn a return of $12\%$ over the next $40$ years.

a$.$ If Hal makes end$-$of$-$year $$2,200$ deposits into the IRA, how much will he have accumulated in $40$ years when he turns $65?$

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 $30$ 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 $65$ 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 $$2,200$ deposits into the IRA, the amount he will have accumulated by the end of his $65$ th year is $$,($Round to the nearest cent.$)$