$30.$ Nonannual Compounding

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 $8\%$ 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.

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

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You must make a payment of $$1,360\mathrm{.}02$ 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 $8\%$ with quarterly compounding. How large must each of the five payments be$?$

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