Nonannual Compounding It is now January $1.$ You plan to make five deposits of $$100$ each, one every $6$ months, with the first payment being made today. If the bank pays a nominal interest rate of $8\%$ but uses semiannual compounding, how much will be in your account after $8$ years?

You must make a payment of $$2,200$ ten years from today. To prepare for this payment, you will make five equal deposits, beginning today and for the next four quarters, in a bank that pays a nominal interest rate of $12\%,$ quarterly compounding. How large must each of the five payments be$?$