An alien abducts you and offers to return you to Earth if you can solve this problem: You need to save $$2,000$ for a spaceship repair fund. If you save $$100$ per month and the interest rate is $3\%($monthly compounding$),$ how many months will it take to reach your goal?

Question $4$ options:

$3$

$1\mathrm{.}63$

$20$

$19\mathrm{.}54$