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$.$ $$13,500$ in $10$ years at $11$ percent?

Present value $

b$.$ $$17,250$ in $16$ years at $11$ percent?

Present value $

c$.$ $$6,900$ each year for $19$ years at $9$ percent?

Present value $

d$.$ $$9,000$ each year, at the beginning, for $45$ years at $11$ percent?

Present value $

e$.$ $$56,000$ each year for $20$ years at $6$ percent?

Present value $

f$.$ $$56,000$ each year for $20$ years, at the beginning, at $6$ percent?

Present value $