Jeff and Jason spend X dollars to purchase an annuity. Jeff buys a perpetuity$-$immediate, which

makes annual payments of $30.$ Jason buys a $12-$year annuity$-$immediate, also with annual payments.

The first payment is $53,$ with each subsequent payment $k\%$ larger than the previous year's payment.

Both annuities use an annual e$\_$ective interest rate of $k\%.$ Calculate $k.$

A$.5\mathrm{.}00$

B$.\frac{5\mathrm{.}3}{b}ar(3)$

C$.5\mathrm{.}50$

D$.5\mathrm{.}67$

E$.6\mathrm{.}00$