An investor is considering two investment options. Option A offers a $4\%$ annual compound

interest rate, and Option B offers a $3\mathrm{.}75\%$ annual compound interest rate with interest

compounded quarterly.

If the investor plans to invest $$15,000$ for $5$ years, which option gains the most interest?

How much more interest does the better option gain? $($round to the nearest cent$)$ $