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 However when the funds are withdrawn from the IRA the full amount withdrawn is treated as income and is taxed at the individual's current income tax rate.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 Another feature of IRAs that is different from a standard savings account is that funds deposited in an IRA cannot be withdrawn prior to retirement, except upon payment of a substantial penalty.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 4 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: square 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 square 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 Yes, a higher real return seems to increase saving modestly. No, people prefer much higher investment returns in the stock market. 2. psychological theories of saving? Yes, because the funds cannot be withdrawn from an IRA prior to retirement, people are not tempted to withdraw these savings. No, because people don't want their money tied up.

To determine whether Sarah should invest her bonus in an IRA or a regular savings account, we need to calculate the net value of each option after five years, considering taxes.<br /><br />### a. Calculating Net Values<br /><br />**1. IRA Account:**<br /><br />- Initial deposit: $10,000<br />- Interest rate: 4% per year<br />- Time period: 5 years<br />- Tax bracket: 30%<br /><br />First, calculate the future value of the IRA before taxes:<br /><br />\[ \text{Future Value} = P \times (1 + r)^n \]<br /><br />Where:<br />- \( P = \$10,000 \)<br />- \( r = 0.04 \) (4% interest rate)<br />- \( n = 5 \) years<br /><br />\[ \text{Future Value} = 10,000 \times (1 + 0.04)^5 \]<br />\[ \text{Future Value} = 10,000 \times 1.21665 \]<br />\[ \text{Future Value} = 12,166.50 \]<br /><br />When Sarah withdraws the funds, she pays 30% tax on the entire amount:<br /><br />\[ \text{Tax} = 0.30 \times 12,166.50 = 3,649.95 \]<br /><br />Net value after taxes:<br /><br />\[ \text{Net Value} = 12,166.50 - 3,649.95 = 8,516.55 \]<br /><br />Rounded to the nearest dollar: **$8,517**<br /><br />**2. Regular Savings Account:**<br /><br />- Initial deposit: $10,000<br />- Interest rate: 4% per year<br />- Tax bracket: 30%<br /><br />Each year, Sarah pays taxes on the interest earned:<br /><br />Annual interest before tax:<br /><br />\[ \text{Annual Interest} = 10,000 \times 0.04 = 400 \]<br /><br />Annual tax on interest:<br /><br />\[ \text{Annual Tax} = 0.30 \times 400 = 120 \]<br /><br />Net annual interest after tax:<br /><br />\[ \text{Net Annual Interest} = 400 - 120 = 280 \]<br /><br />Calculate the total amount after 5 years:<br /><br />\[ \text{Total Amount} = 10,000 + 5 \times 280 = 11,400 \]<br /><br />Rounded to the nearest dollar: **$11,400**<br /><br />**Comparison:**<br /><br />- IRA net value: $8,517<br />- Regular savings account net value: $11,400<br /><br />Sarah will be better off if she invests in the **regular savings account**.<br /><br />### b. Impact of IRAs on Household Savings<br /><br />**1. Response of saving to changes in the real interest rate:**<br /><br />- **No, there is little increase in real returns from an IRA.**<br /><br />The real return from an IRA may not significantly differ from other investment options, especially when considering inflation and tax implications.<br /><br />**2. Psychological theories of saving:**<br /><br />- **Yes, because the funds cannot be withdrawn from an IRA prior to retirement, people are not tempted to withdraw these savings.**<br /><br />The restriction on early withdrawals can help individuals commit to long-term savings, aligning with psychological theories that suggest people save more when access to funds is limited.