Tax-deferred annuities pay no taxes on the income placed into the account, but then pay taxes on all the money when it is withdrawn. Nondeferred plans pay taxes on the income prior to depositing the money into the account, and then only pay taxes on the interest earned by the account. The table below shows the amount set aside in an ordinary annuity each month, the current tax rate, the number of years that contributions will be made to the annuity, and the tax rate when withdrawals from the annuity are made. Complete parts a through c.

a. Find the value of the tax-deferred and the nondeferred accounts. To find the future value of each account, use the formula for finding the future value of an ordinary annuity below, where R is the monthly payment amount, r is the annual rate, m is the number of compounding periods in a year, and n is the number of periods that pass.

b. Calculate the interest that was earned in both accounts. This will be the value of the account minus the payments made. To find the amount of interest earned on each account, first compute the sum of all the payments made to that account by multiplying the amount of the payment by the number of periods n. Subtract this value from the future value to determine the amount of interest earned.

c. If all money is withdrawn from each account and the relevant taxes are paid, which account is better and by how much? Calculate the amount in taxes paid on each account when the funds are withdrawn. Recall that the tax-deferred account pays taxes on the entire amount, while the nondeferred account only pays taxes on the interest earned. Then subtract the amount paid in taxes from the future value of the account to determine the value of each account after taxes. Use these values to determine which account returns more money and the absolute difference between the values of the accounts.

\begin{tabular}{|c|c|c|c|c|} \hline \begin{tabular}{c} Monthly \\ Payment \end{tabular} & \begin{tabular}{c} Number of \\ Years \end{tabular} & \begin{tabular}{c} Annual Interest \\ Rate \end{tabular} & \begin{tabular}{c} Current Tax \\ Rate \end{tabular} & \begin{tabular}{c} Future Tax \\ Rate \end{tabular} \\ \hline$350 & 15 & 9% & 31% & 31% \\ \hline \end{tabular}