Question

1.a.[6] A taxpayer with a 25% marginal tax rate deposits $1000 in a traditional I.R.A., uses it to buy shares in a mutual fund, and holds the shares for 20 years. When the shares are sold, the taxpayer's marginal tax rate is still 25%. Explain why the $1000 I.R.A. deposit earns a higher gross after-tax rate of return than if it were not deposited in a tax sheltered account, but were used to buy the same number of shares of the same mutual fund and held for the same 20 years. b.[5] Suppose the mutual fund shares bought with $1000 in part a increase in value by 7% each year. What is their total pretax value at the end of 20 years? Explain how to derive the answer. c.[5] Under the assumptions of parts a and b, compare the gross after-tax rate of return of 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 20 years. Explain. (The gross after-tax rate of return is the gross after-tax return divided by the net cost of the deposit. The net cost of the deposit is the amount deposited minus the reduction in tax if the deposit can be subtracted from taxable income.) d.[5] Suppose another taxpayer deposits $1000 in a traditional I.R.A., uses it to buy mutual fund shares and sells those shares after 20 years. Explain how it is possible that the taxpayer gets a lower gross after-tax rate of return than if the $1000 used to buy the same shares, held for the same 20 years, but not in an I.R.A. or other tax shelter.

Answer 1

1.a.[6] : The $1000 I.R.A. deposit earns a higher gross after -tax rate of return if it were not deposited in a tax sheltered account, but were used to buy the same number of shares of the same mutual fund and held for the same 20 years because of increasing the Closing price of the shares. Let us explain with an example:

Suppose we have bought a share of XYZ Company for $40 at the beginning of the year. During the year, its price fluctuates, but it closes the year at $44, which represent a increase in percentage return on the investment of 10% ($4/40)or Gross after-tax rate of return is 7.5% (10%(1-25%)).

b.[5] : The Total pretax value at the end of 20 Years is computed by the following formula:

A = P * (1+r/t) ^ (nt)

Where

A= amount after time t

P= principal amount (initial investment)

r= annual percentage increase value ( divide the number by 100)

t= number of years

n= number of times the percentage increase value compounded per year

The total pretax value at the end of 20 Years will be

= $1000(1+.07)^20 = $3869.68.