Final answer:
The final payoff after tax depends on the type of account: for regular savings account and traditional retirement account, the final payoff is $280.33 after 40 years at 5% interest rate and with 35% income tax rate; for a Roth account, the final payoff is $432.19.
Step-by-step explanation:
(a) To calculate the final payoff after tax if $100 pre-tax income is invested in a regular savings account, we need to consider the interest rate and the income tax rate. The interest rate is 5%, so the $100 will grow to $100 * (1 + 0.05) ^ 40 = $432.19 after 40 years. The income tax rate is 35%, so the final payoff after tax will be $432.19 * (1 - 0.35) = $280.33.
(b) If $100 pre-tax income is invested in a retirement account, the final payoff after tax will depend on the type of retirement account. Assuming it is a traditional retirement account, the tax on investment income is deferred until withdrawal. So the $100 will grow to $100 * (1 + 0.05) ^ 40 = $432.19. At retirement, the withdrawal will be subject to income tax at 35%, resulting in a final payoff after tax of $432.19 * (1 - 0.35) = $280.33.
(c) If $100 pre-tax income is invested in a Roth account, the contributions are made with after-tax dollars. So there will be no tax on investment income or withdrawal. The $100 will grow to $100 * (1 + 0.05) ^ 40 = $432.19, and this will be the final payoff after tax as well.