Find the present values of the following ordinary annuities:
a. PV of $400 each six months for five years at a simple rate of 12 percent, compounded semiannually
b. PV of $200 each three months for five years at a simple rate of 12 percent, compounded quarterly
c. The annuities described in parts (a) and (b) have the same amount of money paid into them during the five-year period and both earn interest at the same simple rate, yet the present value of the annuity in part (b) is $31.46 greater than the one in part (a). Why does this occur?