Individual retirement accounts $($IRAs$)$ were established by the U$.$S$.$ government to encourage saving. An individual who deposits part of current earnings in an IRA does not have to pay income taxes on the earnings deposited, nor are any income taxes charged on the interest earned by the funds in the IRA. However, when the funds are withdrawn from the IRA, the full amount withdrawn is treated as income and is taxed at the individual's current income tax rate.

In contrast, an individual depositing in a non$-$IRA account has to pay income taxes on the funds deposited and on interest earned in each year but does not have to pay taxes on withdrawals from the account. Another feature of IRAs that is different from a standard savings account is that funds deposited in an IRA cannot be withdrawn prior to retirement, except upon payment of a substantial penalty.

a$.$ Sarah, who is five years from retirement, receives a $$10,000$ bonus at work. She is trying to decide whether to save this extra income in an IRA account or in a regular savings account. Both accounts earn $9$ percent nominal interest, and Sarah is in the $30$ percent tax bracket in every year $($including her retirement year$).$

Compare the amounts that Sarah will have in five years under each of the two saving strategies, net of all taxes. Is the IRA a good deal for Sarah?

Instructions: Enter your responses rounded to the nearest dollar.

If Sarah invests in the IRA, her net value $($after withdrawing the funds and paying her taxes$)$ five years from now will be: $

If Sarah invests in the normal savings account, her net value $($after taxes$)$ five years from now will be: $

Sarah will be better off if she invests in the Click to select$)$ $$.$

b$.$ Would you expect the availability of IRAs to increase the amount that households save in light of:

$(1)$ the response of saving to changes in the real interest rate?

Yes, the government matches the IRA savings making it very attractive.

No$,$ there is little increase in real returns from an IRA.

No$,$ people prefer much higher investment returns in the stock market.

Yes, a higher real return seems to increase saving modestly.