You are negotiating to make a $7-$year loan of $$22,500$ to Breck Inc. To repay you, Breck will pay $$2,500$ at the end of Year $1,$ $$5,000$ at the end of Year $2,$ and $$7,500$ at the end of Year $3,$ plus a fixed but currently unspecified cash flow, X$,$ at the end of each year from Year $4$ through Year $7.$ Breck is essentially riskless, so you are confident the payments will be made. You regard $8\%$ as an appropriate rate of return on a low risk but illiquid $7-$year loan. What cash flow must the investment provide at the end of each of the final $4$ years, that is$,$ what is X$?$

Group of answer choices

$$3,782\mathrm{.}32$

$$4,500\mathrm{.}96$

$$4,538\mathrm{.}78$

$$2,950\mathrm{.}21$

$$4,576\mathrm{.}61$