Almost every installment loan in the US, from a personal loan to a car loan to a 30-year mortgage, uses the same math to set the monthly payment. Once you know the formula, you can check any lender's quote, compare offers and see exactly how much a loan will cost before you sign. This guide walks through the formula, a full worked example, payments for common loan sizes, and how extra payments and fees change the picture.
The loan payment formula
For a fixed-rate loan with equal payments, the payment is:
Payment = P × r × (1 + r)n ÷ [(1 + r)n − 1]
- P is the principal, the amount you borrow.
- r is the interest rate per payment period. For monthly payments, divide the annual rate by 12. A 6.5% annual rate becomes 0.065 ÷ 12 = 0.0054167 per month.
- n is the total number of payments. A 5-year loan with monthly payments has 5 × 12 = 60 payments.
This is called the annuity or amortization formula. It finds the one payment amount that, paid every month, covers the interest on the remaining balance and brings the balance to exactly zero on the last payment.
Step-by-step example
Say you borrow $25,000 at 6.5% for 5 years.
- Monthly rate: r = 0.065 ÷ 12 = 0.0054167.
- Number of payments: n = 60.
- Growth factor: (1 + r)60 = 1.005416760 ≈ 1.3828.
- Top of the formula: 25,000 × 0.0054167 × 1.3828 ≈ 187.26.
- Bottom of the formula: 1.3828 − 1 = 0.3828.
- Payment: 187.26 ÷ 0.3828 ≈ $489.15 a month.
Over 60 months you pay 60 × $489.15 = $29,349, so the loan costs $4,349 in interest. You can check the result, and see every payment, in the loan calculator.
Payments for common loans
The table shows how the same formula plays out for typical loan sizes. Notice how the term changes the total interest far more than it changes the payment.
| Loan | Amount | Rate | Term | Monthly payment | Total interest |
|---|---|---|---|---|---|
| Personal loan | $10,000 | 12% | 3 years | $332.14 | $1,957 |
| Personal loan | $25,000 | 6.5% | 5 years | $489.15 | $4,349 |
| Auto loan | $35,000 | 7% | 5 years | $693.04 | $6,583 |
| Auto loan | $35,000 | 7% | 6 years | $596.72 | $7,964 |
| Mortgage (P&I) | $300,000 | 6.5% | 15 years | $2,613.32 | $170,398 |
| Mortgage (P&I) | $300,000 | 6.5% | 30 years | $1,896.20 | $382,633 |
Stretching the $35,000 car loan from 5 to 6 years lowers the payment by about $96, but adds $1,381 of interest. On the mortgage, the 30-year term costs more than twice as much interest as the 15-year term. Before choosing a longer term just for the lower payment, check what fits your budget with the car affordability calculator or your mortgage numbers with a lender. Mortgage payments above include principal and interest only; property tax, homeowners insurance and PMI come on top.
How each payment is split
The payment stays the same, but its contents change every month. Interest is always charged on the current balance, so at the start most of the payment goes to interest. Here are the first three payments of the $25,000 loan:
| Payment | Interest | Principal | Remaining balance |
|---|---|---|---|
| 1 | $135.42 | $353.74 | $24,646.26 |
| 2 | $133.50 | $355.65 | $24,290.61 |
| 3 | $131.57 | $357.58 | $23,933.03 |
To build the table yourself, repeat three steps for every month:
- Interest = remaining balance × monthly rate. For payment 1: $25,000 × 0.0054167 = $135.42.
- Principal = payment − interest. $489.15 − $135.42 = $353.74 (the payment is $489.155 before rounding).
- New balance = old balance − principal. $25,000 − $353.74 = $24,646.26.
This list of rows is the amortization schedule. By the last payment, only about $2.64 of the $489.15 is interest. On a 30-year mortgage the effect is even stronger: at 6.5%, more than 80% of each payment goes to interest during the first five years.
Calculating it in Excel or Google Sheets
Spreadsheets have the formula built in:
=PMT(rate per period, number of payments, −loan amount)
For the example: =PMT(6.5%/12, 60, -25000) returns $489.15. The loan amount is entered as a negative number so the payment comes out positive. Two related functions are useful for schedules: =IPMT(6.5%/12, 1, 60, -25000) gives the interest part of payment 1 ($135.42), and =PPMT(6.5%/12, 1, 60, -25000) gives the principal part ($353.74). Change the second argument to see any other month.
What extra payments do
Any amount you pay above the scheduled payment goes straight to principal. The balance drops faster, so every later payment carries less interest, and the loan ends early.
- $25,000 personal loan, 6.5%, 5 years: paying $100 extra each month ends the loan after 49 payments instead of 60 and saves about $865 in interest.
- $300,000 mortgage, 6.5%, 30 years: paying $200 extra each month ends the loan after 277 payments, about 23 years, and saves roughly $103,000 in interest.
The earlier the extra payment, the bigger the saving, because it removes principal that would otherwise collect interest for many years. Before you start, confirm that your lender applies extra money to principal rather than to the next payment, and that there is no prepayment penalty. To model a one-time lump sum or a recurring extra amount on an existing loan, use the loan overpayment calculator.
Interest rate vs. APR
The formula uses the interest rate, but the true cost of borrowing also includes fees. Many personal loans charge an origination fee, often 1% to 10% of the amount, usually deducted from the money you receive. With a 5% fee on the $25,000 loan, you receive $23,750 but still repay 60 payments of $489.15. Measured against the cash you actually got, the cost is about 8.66% APR, not 6.5%.
That is why lenders must show the APR under the Truth in Lending Act, and why APR, not the interest rate, is the number to compare between offers. If you only know a periodic rate and want the annual equivalent, the monthly interest rate calculator converts between them.
Loans that work differently
The formula covers fixed-rate installment loans. A few common products follow other rules:
- Adjustable-rate mortgages (ARMs). The formula applies during each fixed period, but when the rate resets, the payment is recalculated on the remaining balance and remaining term.
- Interest-only loans and HELOCs in the draw period. The payment is just balance × monthly rate. A $50,000 HELOC balance at 8.5% costs about $354 a month in interest, and the principal does not go down at all until repayment starts.
- Credit cards. There is no fixed term. The minimum payment is usually a small percentage of the balance plus interest, so paying only the minimum can take many years.
- Simple-interest auto loans. Many car loans accrue interest daily. The scheduled payment comes from the same formula, but paying a few days early or late shifts slightly more or less of each payment to principal.
For any of these, run the fixed-rate numbers as a baseline and then ask the lender how the actual product differs.
Common mistakes
- Using the annual rate as r. Plugging 0.065 instead of 0.065 ÷ 12 into the formula gives a payment many times too high.
- Counting years instead of payments. n is the number of payments: 60 for a 5-year monthly loan, not 5.
- Comparing payments instead of total cost. A lower payment over a longer term almost always means more interest.
- Ignoring fees. Two loans with the same rate can have very different APRs.
- Forgetting escrow on a mortgage. The formula gives principal and interest only. Taxes and insurance can add hundreds of dollars a month.
Enter your amount, rate and term to get the payment, payoff date and full amortization schedule, with optional extra payments and fees.
Open the loan calculator →FAQ
What is the formula for a monthly loan payment?
Payment = P × r × (1 + r)n ÷ [(1 + r)n − 1], where P is the loan amount, r is the annual rate divided by 12 and n is the number of monthly payments.
How much is the payment on a $25,000 loan?
At 6.5% for 5 years, about $489 a month. At 10% for 5 years it would be about $531, and at 6.5% for 3 years about $766.
How is amortization calculated?
Each month, interest equals the remaining balance times the monthly rate. The rest of the fixed payment reduces the principal. The new balance is used for the next month, and the process repeats until the balance reaches zero.
Is it better to have a lower payment or a shorter term?
A shorter term costs much less in total interest, but the payment is higher. Choose the shortest term whose payment you can comfortably afford, and keep the option to pay extra when you can.
Does paying extra on a loan reduce the payment?
Usually no. On most installment loans, extra payments shorten the term instead of lowering the monthly amount. Some lenders will recast a mortgage, recalculating a lower payment after a large lump sum, often for a fee.
Why is my lender's payment slightly different?
Lenders may count interest daily instead of monthly, start the first payment after an odd number of days, or round each payment. These differences are usually a few cents to a few dollars a month.