Loan Monthly Payment Calculator

Formula

M = Pj/(1−(1+j)^−n)

Worked example

With Loan amount: 250000 currency units, Annual interest rate: 5 %, Loan term: 30 years, Extra monthly principal payment: 0 currency units, Upfront fee paid separately: 0 currency units, monthly payment is 1,342.05 currency units.

How the monthly payment is calculated

Let P be the original loan amount, j the annual interest rate divided by 12 after converting percent to a decimal, and n the number of monthly payments (years × 12). The level monthly payment is M = P × j ÷ [1 − (1 + j)^−n]. If the interest rate is zero, M = P ÷ n.

For 250,000 at a 5% nominal annual rate over 30 years, the scheduled payment is about 1,342.05 currency units per month. With the extra-payment and fee fields set to zero, the total paid is about 483,139 and interest is about 233,139. The schedule computes interest on each remaining balance, applies the scheduled payment plus any extra principal payment, and reduces the final payment to the exact amount still owed. Change the term to see why a smaller monthly payment can still mean more lifetime interest.

What happens inside a payment

Interest for a month is calculated on the balance still owed. At the start of this example, approximately 1,041.67 of the first payment is interest (250,000 × 0.05 ÷ 12), leaving about 300.38 to reduce principal. As the balance falls, less of a fixed payment goes to interest and more goes to principal. This is amortization.

Extra principal and upfront costs

A positive extra payment is added to the scheduled monthly payment and applied to principal after that month’s interest. Lower principal can shorten payoff and reduce later interest. The reported monthly payment is still the original scheduled principal-and-interest amount; inspect the schedule for the actual higher payments and adjusted final payment. The upfront fee is treated as a separate cash payment and included in the total paid. It is not financed, earns no interest in this model, and does not change the monthly payment.

Interest rate versus APR

Use the loan’s stated interest rate for this simplified monthly payment formula. Annual percentage rate (APR) can include loan fees as well as interest, so dividing a disclosed APR by 12 does not necessarily reproduce the lender’s scheduled principal-and-interest payment. The definition and disclosure of APR can also vary by country; check the terms of the actual offer.

What the estimate leaves out

The model assumes a fixed rate, regular on-time monthly payments, and any extra payment going directly to principal without a prepayment penalty. Insurance, tax, escrow, other fees, delayed payments, rate changes, daily interest accrual, and lender-specific rounding are omitted. The fee field is a simple separately paid upfront amount, not a regulatory APR calculation. A mortgage or vehicle payment may include some of those additional amounts. Compare loan offers using their full disclosures and total cost, not only this scheduled payment.

Common questions

Why is the first payment mostly interest?

Interest is charged on the outstanding balance, which is largest at the beginning. Each principal payment reduces the balance used for later interest calculations.

Does the result include tax, insurance, or fees?

The optional upfront fee is included in the total paid, but not in the scheduled monthly principal-and-interest payment. Taxes, insurance and other charges are not modeled.

Can I enter APR as the annual interest rate?

The formula expects a nominal loan interest rate under its monthly-rate assumption. An APR that includes fees is a broader borrowing-cost measure and may not produce the scheduled payment when divided by 12.

Sources and references

• CFPB: How does paying down a mortgage work?
• CFPB: Auto loan key terms, including APR and amortization
• CFPB: How loan amortization works