An investment offers $$4,270$ per year for $15$ years, with the first payment occurring one year from now.

a$.$ If the required return is $6$ percent, what is the value of the investment?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

b$.$ What would the value be if the payments occurred for $40$ years?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

c$.$ What would the value be if the payments occurred for $75$ years?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

d$.$ What would the value be if the payments occurred forever?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$