$($Present value of a perpetuity$)$ At a discount rate of $13\mathrm{.}00\%,$ find the present value of a perpetual payment of $$2,500$ per year. If the discount rate were lowered to $6\mathrm{.}50\%,$ half the initial rate, what would be the value of the perpetuity?

a$.$ If the discount rate were $13\mathrm{.}00\%,$ the present value of the perpetuity is $ $($Round to the nearest cent.$)$

b$.$ If the discount rate were lowered to $6\mathrm{.}50\%,$ half the initial rate, the present value of the perpetuity is $ $($Rouridio the nearest cent.$)$