How much would you have to invest today to receive
a. $12,000 in 6 years at 12 percent?
b. $15,000 in 15 years at 8 percent?
c. $5,000 each year for 10 years at 8 percent?
d. $5,000 each year, at the beginning, for 10 years at 8 percent?
e. $50,000 each year for 50 years at 7 percent?
f. $50,000 each year for 50 years, at the beginning, at 7 percent?