Suppose the interest rate is $5\%,$ the income tax rate $35\%,$ the tax rate on investment

income is $20\%,$ and the investment horizon $40$ years.

$($a$)$ What is the final payoff after tax if $$100$ pre$-$tax income is invested in a regular

savings account?

$($b$)$ What is the final payoff after tax if $$100$ pre$-$tax income is invested in a retirement

account?

$($c$)$ What is the final payoff after tax if $$100$ pre$-$tax income is invested in a Roth account?