Yuki $($age $45$ at year$-$end$)$ has been contributing to a traditional IRA for years $($all deductible contributions$),$ and her IRA is now worth $$40,000.$ She is trying to decide whether she should convert her traditional IRA into a Roth IRA. Her current marginal tax rate is $24$ percent. She plans to withdraw the entire balance of the account in $20$ years, and she expects to earn a before$-$tax rate of return of $5$ percent on her retirement accounts and a $4$ percent after$-$tax rate of return on all investments outside of her retirement accounts. For each of the following alternative scenarios, indicate how much more or less Yuki will accumulate after taxes in $20$ years if she converts her traditional IRA into a Roth IRA. Be sure to include the opportunity cost of having to pay taxes on the conversion.

a$.$ When she withdraws the retirement funds in $20$ years, she expects her marginal tax rate to be $35$ percent.

Answer is complete but not entirely correct.

b$.$ When she withdraws the retirement funds in $20$ years, she expects her marginal tax rate to be $18$ percent.

c$.$ When she withdraws the retirement funds in $20$ years, she expects her marginal tax rate to be $18$ percent. Assume that she earns a $3$

percent after$-$tax rate of return on investments outside of the retirement accounts.