$($Related to Checkpoint $5\mathrm{.}2)($Future value$)$ Leslie Mosallam, who recently sold her Porsche, placed $$9,000$ in a savings account paying annual compound interest of $5$ percent.

a$.$ Calculate the amount of money that will accumulate if Leslie leaves the money in the bank for $2,6,$ and $16$ year$($s$).$

b$.$ Suppose Leslie moves her money into an account that pays $7$ percent or one that pays

$9$ percent. Rework part $($a$)$ using $7$ percent and $9$ percent.

c$.$ What conclusions can you draw about the relationship between interest rates, time, and future sums from the calculations you just did?

a$.$ After placing $$9,000$ in a savings account paying annual compound interest of $5$ percent, the amount of money that will accumulate if Leslie leaves the money in the bank for $2$ year$($s$)$ is $

$($Round to the nearest cent.$)$

If she leaves the money in the bank for $6$ years, the amount of money that will accumulate is $

$($Round to the nearest cent.$)$

If she leaves the money in the bank for $16$ years, the amount of money that will accumulate is $ $($Round to the nearest cent.$)$

b$.$ If Leslie moves her money into an account that pays $7$ percent compounded annually for $2$ year$($s$),$ the amount of money that will accumulate is $

$($Round to the nearest cent.$)$

If Leslie moves her money into an account that pays $7$ percent compounded annually for $6$ years, the amount of money that will accumulate is $$.($Round to the nearest cent.$)$