$1$a$.$ What is the value today of $$6,000$ per year, at a discount rate of $7$ percent, if the first payment is received three years from today and the last payment is received $25$ years from today?

$2.$

A $6-$year annuity of twelve $$8,600$ semiannual payments will begin $11$ years from now, with the first payment coming $11\mathrm{.}5$ years from now.

a$.$

If the discount rate is $15$ percent compounded monthly, what is the value of this annuity five years from now? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ If the discount rate is $15$ percent compounded monthly, what is the value three years from now? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ If the discount rate is $15$ percent compounded monthly, what is the current value of the annuity?