How a loan payment is calculated
Most personal loans, car loans and student loans are amortizing: you repay them in equal payments, and each payment covers that period’s interest first, then pays down the balance. The level payment comes from one formula:
P = amount borrowed · r = yearly rate ÷ payments per year · n = number of payments
With monthly payments, r is the yearly rate divided by 12. With payments every two weeks it is divided by 26, and with weekly payments by 52. If the rate is 0%, the payment is simply P ÷ n.
Worked example
You borrow $25,000 at 8% for 5 years, paid monthly.
- r = 0.08 ÷ 12 = 0.0066667 and n = 5 × 12 = 60
- M = 25,000 × 0.0066667 ÷ (1 − 1.0066667^−60) = $506.91 a month
- Total paid: $506.91 × 60 = $30,414.59, so the interest is $5,414.59
The first payment includes $166.67 of interest (25,000 × 0.0066667) and only $340.24 of principal. As the balance falls, the interest part shrinks and more of each payment goes to principal. The amortization schedule above shows this payment by payment.
How much can you borrow?
Flip the formula around and you can start from the payment you can afford:
At 8%, here is what $500 a month repays over different terms:
| Term | Loan you can repay | Interest paid |
|---|---|---|
| 3 years | $15,955.90 | $2,044.10 |
| 4 years | $20,480.96 | $3,519.04 |
| 5 years | $24,659.22 | $5,340.78 |
| 6 years | $28,517.26 | $7,482.74 |
| 7 years | $32,079.63 | $9,920.37 |
A longer term lets you borrow more for the same payment, but the interest climbs quickly. For a car, a long loan can also leave you owing more than the car is worth. The calculator gives the mathematical maximum; a lender will also check your income, debts and credit history.
Monthly, every two weeks or weekly?
Paying more often means each payment reduces the balance a little sooner, so you pay slightly less interest. Here is $20,000 at 7% over 5 years:
| Frequency | Payments | Each payment | Total interest |
|---|---|---|---|
| Monthly | 60 | $396.02 | $3,761.44 |
| Every two weeks | 130 | $182.54 | $3,730.39 |
| Weekly | 260 | $91.22 | $3,717.07 |
The difference is small because the yearly total is about the same. The big savings come from an accelerated plan: paying half the monthly amount ($198.01) every two weeks. There are 26 two-week periods in a year, so that adds up to 13 monthly payments instead of 12. In this example, it clears the loan after 119 payments, about 4 years 7 months, and cuts interest to $3,372.63.
Interest rate vs APR: what fees really cost
The interest rate decides your payment. The APR (annual percentage rate) also counts upfront costs such as an origination fee, so it shows the true yearly cost. It is the rate at which your payments are worth exactly the money you actually received.
Say the $20,000 loan at 7% comes with a $500 fee taken out of the loan. You still repay $396.02 a month on $20,000, but you only received $19,500. That makes the APR 8.07%, more than a full point above the advertised rate. Add the fee in the Upfront fees section to see your own APR. In the US, Regulation Z sets out this method (the actuarial method in its Appendix J), which is why APRs from different lenders can be compared fairly.
Want to see the payment formula worked through by hand, and how a flat rate compares with a reducing balance? Read how EMI is calculated: an EMI is the same fixed monthly payment this calculator shows.
Tips before you sign
- Compare total cost, not just the payment. A lower payment over a longer term usually costs more overall.
- Check for prepayment penalties. Paying extra early saves the most interest, so make sure your loan allows it.
- Shop by APR. Two loans with the same rate can have very different fees.
- Know your budget. See what you actually take home with the paycheck calculator before you commit to a payment.
Buying a home? The mortgage calculator adds property tax, insurance and PMI. Borrowing in India or Pakistan? The EMI calculator shows processing fees and prepayment the way banks there present them. To see what the same money could earn instead, try the compound interest calculator.
All figures keep full precision. Lenders round each payment to the cent, so your last payment may differ by a few cents.