It is now January $1.$ You plan to make a total of $5$ deposits of $$400$ each, one every $6$ months, with the first payment being made today. The bank pays a nominal interest rate of $10\%$ but uses semiannual compounding. You plan to leave the money in the bank for $10$ years. Do not round intermediate calculations. Round your answers to the nearest cent.

a$)$ How much will be in your account after $10$ years?

b$)$ You must make a payment of $$1,508\mathrm{.}04$ in $10$ years. To get the money for this payment, you will make five equal deposits, beginning today and for the following $4$ quarters, in a bank that pays a nominal interest rate of $10\%$ with quarterly compounding. How large must each of the five payments be$?$