Question

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 However, when the funds are withdrawn from the IRA, the full amount withdrawn is treated as income and is taxed at the individual’s current income tax rate.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 Another feature of IRAs that is different from a standard savings account is that funds deposited in an IRA cannot be withdrawn prior to retirement, except upon payment of a substantial penalty.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 1 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 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)  IRA  regular OR savings account  .


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?  (Click to select)  Yes  No  .

(2) psychological theories of saving?  (Click to select)  No  Yes .

Answer 1

Answer :

In IRA, Net value after 5 years:

(a) :- 10000(1.03)⁵ - 30% = 10000(1.159274) - 30% = 0.7 * 11592.74 = 8114.92

In Regular Savings account :

In first year, tax will be applied on deposit amount of 10000 and the interest earned.

From second year, tax will be applied on interest earned.

Value after 1st year = 10000(1.03) - 30% = 10300*0.7 = 7210

Value after 2nd year = 7210(1.03) - 0.3*0.03*7210 = 1.021*7210 = 7361.41

Value after 3rd year = 1.021* 7361.41 = 7516

Value after 4th year = 1.021*7516 = 7673.84

(b) :- Value after 5th year = 1.021* 7673.84 = 7835

(c) :- Sarah will be Better off investing in IRA.

(d) :- Yes, the saving in IRA will increase owing to stable rate of return. The decrease of rate in Regular savings rate can reduce the amount of interest earned.

(e) :- Psychologically Saving is the key thought of people nearing retirement. In such a scenario, IRAs provide a good deal for increment of wealth.