Answer :
We are given that a car loan can be paid by $250 per month payments. To determine the amount of the loan we can use the following formula:
[tex]P_0=\frac{d(1-(1+\frac{r}{k})^{-kt})}{\frac{r}{k}}[/tex]Where:
[tex]\begin{gathered} P_0=\text{ amount of the loan} \\ r=\text{ interest rate in decimal form} \\ k=\text{ number of compounding periods} \\ t=\text{ time} \\ d=\text{ }monthly\text{ payments} \end{gathered}[/tex]The interest is compounded monthly we have that:
[tex]k=12[/tex]Now, we convert the interest rate into decimal form by dividing both sides by 100:
[tex]r=\frac{3}{100}=0.03[/tex]Now, we plug in the values:
[tex]P_0=\frac{(250)(1-(1+\frac{0.03}{12})^{-(1)(5)})}{\frac{0.03}{12}}[/tex]Solving the operations:
[tex]P_0=13913.09[/tex]Therefore, the amount of the loan is $13913.09