Payment Calculator
Calculate periodic loan payments.
Step-by-Step Solution
About Payment Calculator
Calculate periodic loan payments. This calculator provides instant results with step-by-step explanations to help you understand the calculation process.
Formula
M = P × r(1+r)^n / ((1+r)^n − 1)
How to use this calculator
- Enter the loan amount, annual interest rate, loan term, and payment frequency if the calculator asks for them.
- Check whether the rate is given as an annual percentage rate, because the calculator may need it converted to a per-payment rate.
- Make sure the term matches the payment schedule, for example years for monthly payments.
- Click calculate to see the periodic payment and any related details such as total paid or total interest.
The formula explained
This calculator finds the fixed periodic payment on an amortized loan, where each payment covers both interest and principal. The standard formula uses the loan amount, the interest rate per payment period, and the total number of payments.
- P = loan principal, the amount borrowed
- r = interest rate per payment period written as a decimal
- n = total number of payments
- A = periodic payment amount
Step by step method
- Convert the annual interest rate to a rate per payment period, for example monthly rate equals annual rate divided by 12 when the rate is nominal and payments are monthly.
- Find the total number of payments, for example 5 years with monthly payments gives 60 payments.
- Substitute the values into the payment formula and evaluate the expression to get the fixed payment amount.
Worked example
Problem. You borrow 12000 at an annual interest rate of 6 percent for 3 years, with monthly payments. What is the monthly payment?
- Convert the rate to a monthly decimal rate: r = 0.06/12 = 0.005.
- Find the total number of payments: n = 3 12 = 36.
- Use the loan payment formula, A = P(r(1+r)^n)/((1+r)^n - 1), so A = 12000(0.005(1.005)^{36})/((1.005)^{36} - 1) 365.23.
Answer. $365.23 per month
Tips and common mistakes
- A small change in the interest rate can noticeably change the payment, so always check whether the rate is annual, monthly, or already converted.
- If your loan has fees, extra payments, or a different compounding schedule, the basic payment formula may not match the exact lender quote.
Frequently asked questions
How do I use the payment calculator for a loan?+
Enter the loan amount, interest rate, repayment term, and payment frequency if the tool asks for it. The calculator then estimates your regular payment amount, such as monthly, weekly, or biweekly.
What does the periodic payment formula mean?+
A periodic payment is the fixed amount you pay at each interval to repay a loan over time, usually covering both interest and principal. It helps you see how much each payment will be before you borrow.
What happens if I change the interest rate or loan term?+
A higher interest rate usually increases each payment, because more of each installment goes toward interest. A longer loan term usually lowers the payment amount, but you may pay more total interest over the life of the loan.
Why is my payment different from my lender’s quote?+
Lenders may include extra charges such as fees, insurance, taxes, or a different compounding method. This calculator estimates the loan payment itself, so it may not match an all-in monthly bill exactly.
Can this calculator handle edge cases like zero interest or very short terms?+
Yes, a zero interest loan should reduce to simply dividing the loan amount by the number of payments. For very short terms, the payment can look large because the balance must be repaid in fewer installments.
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