Suppose you begin saving for your retirement by depositing $$7,500$ next year in an IRA account. You will increase your payments by $3\%$ each year thereafter $($your deposit two years from now will be $$7,725=$$$7,500*1\mathrm{.}03).$ If the effective annual rate is $9\%,$ how much money will you have $40$ years from now if you stop making payments in $25$ years? $($Hint: be careful with the timing here, the first payment is in year $1$ and the last payment is in year $25.$ You withdraw the money in year $40)$

Group of answer choices

$1,230,124$

$$187,500$

$$94,648\mathrm{.}64$

$$1,231,230$

$$2,972,859$