Chapter 5.3, Problem 34E

In Exercises $31-34$, use the following information. An Individual Retirement Account (IRA) is an annuity that is set up to save for retirement. IRAs differ from TDAs in that an IRA allows the participant to contribute money whenever he or she wants, whereas a TDA requires the participant to have a specific amount deducted from each of his or her paychecks.

If Bo McSwine from Exercise $32$ started her IRA at age $35$ rather than age $16$, how big of an annual contribution would he have had to have made the same amount saved at age $65$?

32. When Bo McSwine was $16$, he got an after-school job at his parents’ barbecue restaurant. His parents told him that if he put some of his earnings into an IRA, they would contribute an equal amount to his IRA. That year and every year thereafter, he deposited $\$900$ into his IRA. When he became $21\text{years}$ old, his parents stopped contributing, but Bo increased his annual deposit to $\$1,800$ and continued depositing that amount annually until he retired at age $65$. His IRA paid $7.75\%$ interest. Find the following:

a. The future value of the account.

b. Bo’s and his parents’ total contributions to the account.

c. The total interest.

d. The future value of the account if Bo waited until he was 18 before he started his IRA.

e. The future value of the account if Bo waited until he was 25 before he started his IRA.