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$.$ $$13,100$ in $9$ years at $9$ percent?

Present value $

b$.$ $$17,000$ in $20$ years at $10$ percent?

Present value $

c$.$ $$6,800$ each year for $20$ years at $6$ percent?

Present value $

d$.$ $$8,000$ each year, at the beginning, for $40$ years at $10$ percent?

Present value $

e$.$ $$55,000$ each year for $50$ years at $10$ percent?

Present value $

f$.$ $$55,000$ each year for $30$ years, at the beginning, at $10$ percent?

Present value $