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$.$ $$15,250$ in $11$ years at $9$ percent?

Present value $

$5910$

b$.$ $$19,600$ in $18$ years at $6$ percent?

Present value $

c$.$ $$8,000$ each year for $14$ years at $8$ percent?

Present value $

d$.$ $$8,000$ each year, at the beginning, for $20$ years at $12$ percent?

Present value $

e$.$ $$65,000$ each year for $20$ years at $10$ percent?

Present value $

f$.$ $$65,000$ each year for $20$ years, at the beginning, at $11$ percent?

Present value $