How much would you have to invest today to receive: (Use a Financial calculator to arrive at the answers. Round the final answers to the nearest whole dollar.)

a. $13,000 in 8 years at 12 percent?

Present value $

b. $16,500 in 19 years at 9 percent?

Present value $

c. $6,700 each year for 17 years at 12 percent?

Present value $

d. $7,000 each year, at the beginning, for 35 years at 9 percent?

Present value $

e. $54,000 each year for 40 years at 9 percent?

Present value $

f. $54,000 each year for 40 years, at the beginning, at 9 percent?

Present value $