You are in negotiations to make a $7-$year loan of $$31,000$ to DeVille Corporation. To repay you, DeVille will pay $$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 $7.$ You are confident the payments will be made, since DeVille is essentially riskless. 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$?$

Select the correct answer.

a$.$ $$7,037\mathrm{.}75$

b$.$ $$7,049\mathrm{.}05$

c$.$ $$7,003\mathrm{.}85$

d$.$ $$7,015\mathrm{.}15$

e$.$ $$7,026\mathrm{.}45$