Shawna wants to buy a new car that costs $25 000. She is given a loan from the bank that has an interest rate of 8.5% per year compounded monthly. Shawna wants to have this loan paid off in 4 years. What is her monthly payment?

1 answer

To calculate Shawna's monthly payment, we need to use the formula for calculating the monthly payment on a loan:

\[ P = \frac{r(PV)}{1-(1+r)^{-n}} \]

Where:
P = monthly payment
r = monthly interest rate (annual interest rate divided by 12)
PV = present value or loan amount
n = total number of payments

First, we need to convert the annual interest rate to a monthly interest rate. Since the interest is compounded monthly, we divide the annual interest rate by 12 and convert it to a decimal:

\[ r = \frac{8.5}{100} รท 12 = 0.0071 \]

Next, we need to calculate the total number of payments:

\[ n = 4 \times 12 = 48 \]

Finally, we can substitute the values into the formula:

\[ P = \frac{0.0071(25000)}{1-(1+0.0071)^{-48}} \]

Calculating this expression will give us Shawna's monthly payment.