a$.$ What is the amount of the annuity purchase required if you wish to receive a fixed payment of $$230,000$ for $15$ years? Assume that the annuity will earn $12$ percent per year.

b$.$ Calculate the annual cash flows $($annuity payments$)$ from a fixed$-$payment annuity if the present value of the $15-$year annuity is $$1\mathrm{.}3$ million and the annuity earns a guaranteed annual return of $12$ percent. The payments are to begin at the end of the current year.

c$.$ Calculate the annual cash flows $($annuity payments$)$ from a fixed$-$payment annuity if the present value of the $15-$year annuity is $$1\mathrm{.}3$ million and the annuity earns a guaranteed annual return of $12$ percent. The payments are to begin at the end of seven years.

$($For all requirements, do not round intermediate calculations. Round your answers to $2$ decimal places. $($e$.$g$.,32\mathrm{.}16))$

$1.$ Present Value $=$ $$1,566,498\mathrm{.}83$

$2.$ Annual cash flows $?$

$3.$ Annual Cash flows $?$