Your sister just deposited $$7,500$ into an investment account. She believes that she will earn an annual return of $9\mathrm{.}2$ percent for the next $10$ years. You believe that you will only be able to earn an annual return of $8\mathrm{.}4$ percent over the same period. How much more must you deposit today in order to have the same amount as your sister in $10$ years?

Multiple Choice

$$572\mathrm{.}25$

$$1,250\mathrm{.}32$

$$53\mathrm{.}27$

$$534\mathrm{.}10$

$$610\mathrm{.}40$