Complete guide
Reviewed July 2026Almost every loan you will ever take — personal, auto, student or home — is an amortizing loan. That means you repay it in equal, scheduled payments, each covering the interest due plus a slice of the principal, until the balance reaches zero. The payment stays the same every month, which makes budgeting easy, but the split between interest and principal shifts steadily as you go.
This calculator turns three inputs — the amount you borrow, the interest rate, and the term — into your exact monthly payment, the total interest you will pay, and the full payoff picture. It uses the same amortization formula banks use, so the payment matches a lender quote to the dollar.
Below we show the formula (including the special case when the rate is zero), explain the crucial difference between the interest rate and APR, and reveal how a shorter term or a few extra payments can save you a surprising amount of interest.
How a loan payment is calculated
The payment comes from the standard amortization (annuity) formula. It solves for the fixed amount that pays the loan off in exactly n payments at rate r.
The formula
M = P × r × (1 + r)^n ÷ ((1 + r)^n − 1) M = monthly payment P = principal (amount borrowed) r = monthly rate = APR ÷ 12 n = number of payments = years × 12 Special case: if r = 0, then M = P ÷ n.
Interest is charged only on the outstanding balance, so as the principal falls, the interest portion of each payment shrinks and the principal portion grows — even though the total payment never changes. This is amortization in action.
Worked example
- Borrow P = $20,000 for a 5-year personal loan at 10% APR.
- Monthly rate r = 0.10 ÷ 12 = 0.008333; number of payments n = 60.
- M = 20,000 × 0.008333 × 1.008333^60 ÷ (1.008333^60 − 1) ≈ $424.94/month.
- Total paid = 424.94 × 60 = $25,496, so total interest ≈ $5,496.
- Shorten to 3 years and the payment rises to ~$645 but total interest drops to about $3,230.
Interest rate vs APR
The interest rate is the cost of borrowing the principal. The APR (annual percentage rate) is broader: it folds in lender fees such as origination charges, so it reflects the true annual cost of the loan. Two loans can share the same interest rate yet have very different APRs once fees are counted — which is why APR is the fairer number for comparing offers.
Why early payments barely dent the balance
- In month one, interest is charged on the full balance, so most of your payment covers interest.
- Only the small leftover reduces principal, so the balance falls slowly at first.
- As the balance drops, less interest accrues and more of each payment attacks the principal.
- This is why extra payments early in a loan save the most interest — they cut the balance that all future interest is charged on.
Paying less interest — and using this tool
- Enter the loan amount, APR and term to see your monthly payment and total interest.
- Compare a shorter term: it raises the payment but can cut total interest sharply.
- Test extra monthly payments — even a small amount early shortens the loan and lowers interest.
- Improve your credit score before applying; a lower APR reduces every payment.
- Watch for origination fees and prepayment penalties, which change the true cost beyond the rate.
Frequently asked questions
Glossary
- Principal
- The amount borrowed and still owed; each payment reduces it.
- Amortization
- Repaying a loan in equal payments that shift from mostly interest to mostly principal over time.
- Interest rate
- The percentage charged on the outstanding principal.
- APR
- Annual percentage rate — the interest rate plus lender fees, reflecting the loan's true annual cost.
- Term
- The length of the loan, usually in months or years.
- Origination fee
- An upfront charge for processing the loan that raises the effective cost.
- Amortization schedule
- A table of each payment's interest, principal and remaining balance.
Key takeaways
Any amortizing loan's payment comes from M = P·r·(1+r)^n ÷ ((1+r)^n − 1); if the rate is zero, M = P ÷ n.
Compare loans by APR, which includes fees, not just the headline interest rate.
A shorter term, extra early payments or a lower APR each cut total interest — sometimes dramatically.
Enter your loan amount, APR and term above to see your monthly payment and total interest, then try a shorter term or extra payment to watch the savings.