What is the monthly payment formula?

Monthly Payment Formula

Calculating monthly loan payments requires understanding the principal amount, annual percentage rate (APR), and loan term in months. The formula for determining the monthly payment is as follows:

Monthly Payment = [P x (r / (1 – (1 + r)^(-nT)))]

where:

• P is the principal amount borrowed
• r is the monthly interest rate (APR / 12)
• n is the number of payments per year (12 for monthly payments)
• T is the number of years for the loan term

Step-by-Step Calculation:

1. Determine the Monthly Interest Rate:

Divide the APR by 12 to get the monthly interest rate.

2. Calculate the Number of Monthly Payments:

Multiply the number of years by 12 to determine the total number of monthly payments.

3. Plug Values into the Formula:

Substitute the principal amount, monthly interest rate, and number of monthly payments into the formula.

4. Solve for Monthly Payment:

Multiply and divide as needed to solve for the monthly payment.

Example:

For a $10,000 loan with an APR of 5% for 5 years:

• Monthly interest rate = 5% / 12 = 0.0042
• Number of monthly payments = 5 years x 12 = 60

Monthly Payment = [10,000 x (0.0042 / (1 – (1 + 0.0042)^(-60)))]
= $208.20

Note: This formula provides an approximate monthly payment, as it does not account for additional fees or charges that may be associated with the loan.