How much would you have to invest today to receive: Use Appendix B and Appendix D$.($Round $"$PV Factor" to $3$ decimal places. Round the final answers to the nearest whole dollar.$)$

a$.$ $$14,200$ in $6$ years at $11$ percent?

Present value $

$7597$

b$.$ $$18,500$ in $20$ years at $9$ percent?

Present value $

$3293$

c$.$ $$7,500$ each year for $15$ years at $13$ percent?

Present value $

d$.$ $$7,500$ each year, at the beginning, for $31$ years at $7$ percent?

Present value $

e$.$ $$60,000$ each year for $50$ years at $10$ percent?

Present value $

f$.$ $$60,000$ each year for $51$ years, at the beginning, at $10$ percent?

Present value $