$1.$ You are scheduled to receive annual payments of $$14,119$ for each of the next $19$ years. Your discount rate is $9\mathrm{.}6$ percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?

$2.$ What is the present value of $$7,928$ a year at a discount rate of $9\mathrm{.}2$ percent if the first payment is received $6$ years from now and you receive a total of $12$ annual payments?