1a.[5] The gross after-taxrate of returnon an investment is the gross after-tax return divided by thenet costof the investment. Thenet costof the investment is the amount invested minus the reduction in tax if the investment can be subtracted from taxable income. A taxpayer with a 22% marginal tax rate deposits $1000 in a traditional I.R.A., using it to buy shares in a mutual fund, and holds the shares for 25 years. When the shares are sold, the taxpayer's marginal tax rate is still 22%. Explain why the I.R.A. deposit earns a higher gross after-tax rate of return than if it was not deposited in a tax sheltered account, but the same $1000 was used to buy the same number of shares of the same mutual fund and held for the same 25 years.

b.[5] Suppose the mutual fund shares bought with $1000 in part a increase in value by 5% each year. What is their total pretax value at the end of 25 years? Explain how to derive the answer.

c.[5] Under the assumptions of parts a and b, compare the gross after-taxrate of returnof the traditional I.R.A. deposit to the gross after-tax rate of return if the $1000 deposit were in a Roth I.R.A. and used to buy the same mutual fund shares, held for the same 25 years. Explain the comparison.