Chapter 8.4, Problem 51E

Tax-deferred annuities work like this: If, for example, you plan to set aside $400 per month for your retirement in 30 years in a tax-deferred plan, the $400 is not taxed now, so all of the $400 is invested each month. In a non deferred plan, the $400 is first taxed and then the remainder is invested. So, if your tax bracket is 25%, after you pay taxes, you would have only 75% of the $400 to invest each month. However, in the tax-deferred plan, all of your money is taxed when you withdraw the money. In the non deferred plan, only the interest that you have earned is taxed.

In Exercises 49-54, we give the amount you are setting aside in an ordinary annuity each month, your current tax rate, the number of years you will contribute to the annuity, and your tax rate when you begin withdrawing from the annuity. Answer the following questions for each situation:

a. Find the value of the tax-deferred and the non deferred accounts.

b. Calculate the interest that was earned in both accounts. This will be the value of the account minus the payments you made.

c. If you withdraw all money from each account and pay the relevant taxes, which account is better and by how much?

Monthly Payment	Number of Years	Annual Interest Rate	Current Tax Rate	Future Tax Rate
$400	20	4%	30%	30%