Compound interest is represented by the following expression:
[tex]\begin{gathered} A=P(1+i)^n \\ A=\text{final amount including principal} \\ P=\text{ principal amount} \\ i=\text{ interest rate per year}(\text{decimal form)} \\ n=\text{ number of years invested} \end{gathered}[/tex]With the information given, we can substitute and get the final amount to be paid:
[tex]\begin{gathered} A=15,000(1+0.075)^7 \\ A=24,885.74 \end{gathered}[/tex]The amound that must be paid back would be $24,885.74
Rounding to the nearest dollar: $24,886
