A couple wants to give their newly born daughter a gift on her ${21}^{st}$ birthday that has a current buying power of $$32,000.$

$($a$)$ Assume an annual effective inflation rate of $5\frac{4}{5}\%.$ How much should they deposit in a trust fund so that at her ${21}^{st}$ birthday it has the buying power of $$32,000$ currently?

$($b$)$ If instead they find a certificate of deposit deal, with an annual interest rate of $5\frac{4}{5}\%$ compounded continuously. What should be the amount of the single payment?