Question

You can afford a $250 per month car payment. You've found a 5 year loan at 3% interest. How big of a loan can you afford?

Answer 1

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:

`P_0=(d(1-(1+(r)/(k))^(-kt)))/((r)/(k))`

Where:

`\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}`

The interest is compounded monthly we have that:

`k=12`

Now, we convert the interest rate into decimal form by dividing both sides by 100:

`r=(3)/(100)=0.03`

Now, we plug in the values:

`P_0=((250)(1-(1+(0.03)/(12))^(-(1)(5))))/((0.03)/(12))`

Solving the operations:

`P_0=13913.09`

Therefore, the amount of the loan is $13913.09