Compute the purchasing power in an IRA versus an IRA that has been converted to a Roth IRA.$$ Please show the steps for how you got your answer.

Compute the following:$$

$1)$ The purchasing power of both the IRA and the converted Roth IRA on the day of the conversion of one of the accounts to a Roth IRA.$$

$2)$ The purchasing power of the IRA and converted Roth IRA $20$ years in the future.

BACKGROUND:

Ricardo and Lucy both have IRAs with identical balances $($$$100,000$ in each$).$ The are both in the $22\%$ marginal tax bracket.$$ Ricardo and Lucy also each have $$32,000$ in savings accounts.$$ Lucy converts her IRA to a Roth IRA today.$$ Ricardo does not.$$

Compute the purchasing power for each of them today $($immediately after Lucy completes the conversion$).$

Based on the assumptions below, forecast the purchasing power each of them will have in their IRA or Roth IRA account $20$ years from today.

ASSUMPTIONS:

$--20$ years from now, Ricardo and Lucy will both be in the $24\%$ marginal tax bracket.

$--$Assume they will both withdraw the full balance$($s$)$ of their IRA and Roth IRA accounts at the end of $20$ years, so that they can spend the money.

$--$Each of their IRA$/$Roth IRA accounts will earn $11\mathrm{.}0\%$ over the next $20$ years.

$--$Each of them will add $$6,000$ per year to their IRA or Roth IRA for the next $20$ years.

$--$Each of their savings accounts will earn zero interest $(0\mathrm{.}00\%)$ over the next $20$ years.

$--$Include the value of the savings accounts in the computation of purchasing power.