Question

1.a. Explain what a traditional I.R.A. is. Explain why $1000 deposited in a traditional I.R.A., used to buy shares of a particular mutual fund, which are held for 10 years, earns a higher gross after-tax return than $1000 of saving not deposited in a tax sheltered account, but used to buy the same number of shares of the same mutual fund, which are also held for 10 years.

b. Suppose that, in part a, the mutual fund shares bought with the $1000 increase in value by 6% each year. What is their total value at the end of 10 years? Explain how you find the answer.

c. Suppose that the taxpayer's marginal income tax rate is 30% when the money in the traditional I.R.A. is withdrawn. Under the assumptions of parts a and b, what is the taxpayer's gross after-tax return from the $1000 traditional I.R.A. deposit at the end of the 10 year holding period when the gross earnings are withdrawn and the tax on them is paid? Explain all your steps in finding this gross after-tax return.

d. Is it possible that the gross after-tax return in part c is higher than the gross after-tax return would be from a $1000 deposit in a Roth I.R.A., used to buy shares in the same mutual fund and held for the same 10 years? Explain.

e. Under what condition would the gross after-tax rate of return on the $1000 deposit in the traditional I.R.A. be bigger than the gross after-tax rate of return on the $1000 deposited in a Roth I.R.A. and used to buy the same mutual fund shares, held for the same 10 years? 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 when the deposit can be subtracted from taxable income. Explain how you get your answer.

f. What seems to be the strongest evidence described in the N10 notes supporting the claim that not all the money deposited in I.R.A. accounts is new personal saving induced by the tax sheltering provided by I.R.A. accounts? List the page(s) and paragraph(s) where the evidence is described. Explain how the evidence supports the claim.  

Answer 1

1)

a)A traditional IRA is a type of individual retirement account that lets your earnings grow tax-deferred. You pay taxes on your investment gains only when you make withdrawals in retirement.If you're not covered by a retirement plan at work, you can deduct the entire amount of your IRA contribution (up to $5,500 annually, or $6,500 if you're 50 or older) on your income tax return. If you are covered by a retirement plan, your income will dictate whether or not your contribution is deductible.

Amount Contributed in Traditional IRA ($1000) is deductble from your income for paying taxes in the year of contribution and Investment gains are taxable in the year of withdrawl and not in the year of Realised.

Therefore if we compare amount contributed in Traditional IRA will grow more and result in higher returns after tax than the savings of $1000 deposited in same stock or mutual funds where funds of Traditional IRA invested since because for Normal Savings amount deposited in non tax deductible mutual funds we can not claim deduction for contrbution and Investment gains are taxable every year there fore Traditional IRA results in higher returns after tax.

b) Amount of $1000 invested in Mutual funds after 10 years with 6% increase every year:

$1000*(1.06)^10 = $1790.85

C) If Marginal Income tax Rate on retirement is 30%:

Gain on Investment in Traditional IRA after 10 years = $1790.85-$1000= $790.85

Gain after Tax = $790.85(1-0.3)=$553.60

d) No. Gross After tax return in Roth IRA = $790.85(Since Investment gains are Tax free)

where as Gross After tax return in Traditional IRA = $ 553.60 which is lower than investment in Roth IRA

e) Net Cost of Deposit in Traditional IRA = $1000(1-0.03)=$700

Gross after tax return in Traditional IRA(after 10 years) = $553.60

Gross after tax rate of return in Traditional IRA = $553.60/700=79%

Net Cost of Deposit in Roth IRA = $1000

Gross after tax return in Roth IRA(after 10 years) = $790.85

Gross after tax rate of return in Roth IRA = $790.85/1000=79%

Condition 1: Gross after tax rate of return in Traditional IRA will be more if marginal tax rate on retirement is less than the marginal tax rate in the year of contribution

For example if Marginal tax rate is 10% in year of retirement and 20% in the year of Contribution

Gross after tax rate of return in Traditional IRA = $(790.85*0.9)/(1000*0.8) =88.97%

Where as Gross after tax rate of return in Roth IRA = 79%