Jeffery has nothing saved for retirement. He wants to receive $$49,000\mathrm{.}00$ per year for $4$ years during retirement. The first of these payments will be received in $7$ years. Jeffery can earn a return of $9\mathrm{.}81$ percent per year. How much does Jeffery need to save each year for $6$ years to have exactly enough to meet his retirement goal if he makes his first annual savings contribution in $1$ year and all savings contributions are equal?

$$22,303\mathrm{.}85($plus or minus $10$ dollars$)$

$$20,311\mathrm{.}31($plus or minus $10$ dollars$)$

$$18,496\mathrm{.}77($plus or minus $10$ dollars$)$

$$18,157\mathrm{.}86($plus or minus $10$ dollars$)$

none of the answers are within $10$ dollars of the correct answer