Tom Huston, 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.

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

b$.$ If Tom 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?

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 Tom$$s sixty$-$fifth year.

d$.$ Rework parts a$,$ b$,$ and c$,$ assuming that Tom 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 Tom$$s sixty$-$fifth year.