Question

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.

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 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.

If Bo McSwine had started his IRA at age 35 rather than age 16, how big of an annual contribution would he have had to have made to have the same amount saved at age 65? (Round answer to the nearest cent.)

$______

Answer 1

Annual contribution to IRA= $1800

Interest rate=7.75%

Time period=65-16+1(Because he also contributed when was 16 years old) =50

Using excel to calculate the FV, we have final amount= $868,553.90

If he started at age 35, then time period=65-35+1= 31 years

So, required annual payment can be calculated using excel as follows:

So, required annual payment= $7744.27