What is the formula for a loan payment?

P = L × r ÷ [1 − (1 + r)−n], where L is the loan amount, r the interest rate per period and n the number of payments.

How do I calculate a monthly payment from an annual rate?

Divide the annual rate by 12 to get r, and multiply the term in years by 12 to get n.

How much interest will I pay in total?

Total interest = payment × number of payments − loan amount.

What if the interest rate is 0%?

The payment is simply the loan amount divided by the number of payments.

Loan Payment Formula and Calculator

Home › Finance Formulas › Loan Payment Formula and Calculator

Loan Payment Calculator

The loan payment formula gives the fixed payment that repays an amortizing loan, such as a car loan, personal loan or fixed-rate mortgage, over a set number of payments. It comes from the present value of an annuity: the amount borrowed must equal the present value of all the payments at the loan’s interest rate. Solving that equation for the payment gives P = L × r ÷ [1 − (1 + r)⁻ⁿ].

Formula

P = L × r1 − (1 + r)⁻ⁿ

Where

P: payment per period
L: loan amount (principal)
r: interest rate per period = annual rate ÷ payments per year
n: total number of payments = years × payments per year

Calculator

Loan amount

Annual interest rate (%)

Loan term (years)

Payments per year

Result and step-by-step solution

Payment per period

483.32

60 monthly payments; total repaid 28,999.20, of which 3,999.20 is interest.

Rate per period and number of payments
r = 6%12 = 0.005; n = 5 × 12 = 60
Discount term
(1 + r)⁻ⁿ = (1 + 0.005)⁻⁶⁰ = 0.7413722
Apply the payment formula
P = 25,000.00 × 0.0051 − 0.7413722 = 483.32
Totals
Total paid = 483.32 × 60 = 28,999.20; interest = 28,999.20 − 25,000.00 = 3,999.20
First payment split
Interest = 25,000.00 × 0.005 = 125.00; principal = 483.32 − 125.00 = 358.32

How to use the formula

The rate r is the rate per payment period (annual rate ÷ payments per year) and n is the total number of payments. The calculator shows both conversions, the discount term, the payment, the total paid and the total interest, and how the very first payment splits between interest and principal.

Borrowing 25,000 at 6% for 5 years with monthly payments costs 483.32 a month, 28,999.20 in total, so 3,999.20 of interest. Of the first payment, 125.00 is interest and 358.32 reduces the balance. To see every payment, open the amortization schedule; to see what you still owe after some payments, use the remaining balance formula. This is the same result as Excel’s PMT(rate/12, years*12, amount).

Frequently asked questions

What is the formula for a loan payment?: P = L × r ÷ [1 − (1 + r)⁻ⁿ], where L is the loan amount, r the interest rate per period and n the number of payments.
How do I calculate a monthly payment from an annual rate?: Divide the annual rate by 12 to get r, and multiply the term in years by 12 to get n.
How much interest will I pay in total?: Total interest = payment × number of payments − loan amount.
What if the interest rate is 0%?: The payment is simply the loan amount divided by the number of payments.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.