$($Present value of a$$ perpetuity$)$At a discount rate of $9\mathrm{.}50\%,$ find the present value of a perpetual payment of $$$$4$ comma $500$ per year. If the discount rate were lowered to $4\mathrm{.}75\%,$ half the initial$$ rate, what would be the value of the$$ perpetuity?

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Part $1$

a$.$ If the discount rate were $9\mathrm{.}50\%,$ the present value of the perpetuity is$$ $

$$

enter your response here. $($Round to the nearest$$ cent.$)$

Part $2$

b$.$If the discount rate were lowered to $4\mathrm{.}75\%,$ half the initial$$ rate, the present value of the perpetuity is$$ $

$$

enter your response here. $($Round to the nearest$$ cent.$)$