You need to have $$31,750$ in $20$ years. You can earn an annual interest rate of $6$ percent for the first $6$ years, $6\mathrm{.}6$ percent for the next $5$ years, and $7\mathrm{.}3$ percent for the final $9$ years. How much do you have to deposit today?

Multiple Choice

$$9,899\mathrm{.}80$

$$8,624\mathrm{.}32$

$$7,743\mathrm{.}93$

$$8,601\mathrm{.}25$

$$6,882,49$