Juliana is taking out an $8,700, 3-year loan with an APR of 2.31%. What will be the monthly payment for this loan? Round to the nearest cent.

To calculate the monthly payment for Juliana's loan, we can use the formula for the monthly payment on an amortizing loan:

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

where:
- $ M $ is the monthly payment,
- $ P $ is the loan principal (amount borrowed, $8,700),
- $ r $ is the monthly interest rate (APR divided by 12 months),
- $ n $ is the total number of payments (loan term in months).

### Step 1: Convert APR to monthly interest rate
The APR is 2.31%, so the monthly interest rate $ r $ is:
\[
r = \frac{2.31\%}{12} = \frac{0.0231}{12} = 0.001925
\]

### Step 2: Calculate the number of payments
Since it's a 3-year loan, the number of monthly payments $ n $ is:
\[
n = 3 \times 12 = 36
\]

### Step 3: Plug values into the formula
Now we substitute $ P = 8700 $, $ r = 0.001925 $, and $ n = 36 $ into the formula:
\[
M = \frac{8700 \cdot 0.001925 \cdot (1 + 0.001925)^{36}}{(1 + 0.001925)^{36} - 1}
\]

Calculating this yields:

\[
M \approx 250.00
\]

### Answer
Juliana's monthly payment will be approximately **$250.00**.

Would you like more details on any of these steps, or do you have any questions?

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Here are some related questions:
1. How would the monthly payment change if the APR increased to 3%?
2. What is the total interest paid over the life of the loan?
3. How does the loan balance change over time with each monthly payment?
4. How much would be saved with a lower APR of 2%?
5. What would the monthly payment be if the loan term were extended to 5 years?

**Tip:** For accuracy, always ensure interest rates are converted to a monthly basis for monthly payments.

Find out how to calculate the monthly payment for an $8,700 loan with a 3-year term and 2.31% APR. This step-by-step solution explains loan amortization and interest rate calculations, making it suitable for high school students in Grades 10-12.

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