Loan Payment Calculator Formula

Understand the math behind the loan payment calculator. Each variable explained with a worked example.

Use the Loan Payment Calculator

Formulas Used

Monthly Payment

monthly_payment = monthly_rate > 0 ? loan_amount * monthly_rate * pow(1 + monthly_rate, num_payments) / (pow(1 + monthly_rate, num_payments) - 1) : loan_amount / num_payments

Total Amount Paid

total_paid = monthly_payment * num_payments

Total Interest

total_interest = total_paid - loan_amount

Variables

VariableDescriptionDefault
loan_amountLoan Amount(USD)25000
annual_rateAnnual Interest Rate(%)7.5
loan_term_yearsLoan Term (Years)(years)5
monthly_rateDerived value= annual_rate / 12 / 100calculated
num_paymentsDerived value= loan_term_years * 12calculated

How It Works

How to Calculate Loan Payments

The loan payment formula determines your fixed monthly payment based on the loan amount, interest rate, and repayment term.

Formula

M = P * [r(1+r)^n] / [(1+r)^n - 1]

Where:

  • M = Monthly payment
  • P = Loan amount (principal)
  • r = Monthly interest rate
  • n = Total number of payments

    • Worked Example

    You take out a $25,000 personal loan at 7.5% annual interest for 5 years.

    loan_amount = 25000annual_rate = 7.5loan_term_years = 5
    1. 01Monthly interest rate: 7.5% / 12 = 0.625% (0.00625)
    2. 02Total payments: 5 * 12 = 60
    3. 03Monthly Payment = $25,000 * [0.00625 * (1.00625)^60] / [(1.00625)^60 - 1]
    4. 04Monthly Payment = $500.57
    5. 05Total paid: $500.57 * 60 = $30,034.20
    6. 06Total interest: $30,034.20 - $25,000 = $5,034.20

    Ready to run the numbers?

    Open Loan Payment Calculator