How Loan Payments Work: Formula, Amortization and Total Cost
Before you take out a personal loan, a car loan or a mortgage, it helps to understand how the monthly payment is calculated and where your money goes each month. This guide explains the loan payment formula, amortization and the factors that change the total cost. To get your own numbers instantly, use the loan repayment calculator.
What is an amortizing loan?
Most consumer loans and mortgages are amortizing: you pay the same amount every month, and each payment covers the interest for that month plus a slice of the principal (the amount you borrowed). By the last payment the balance reaches zero.
The monthly payment formula
M = P × r × (1 + r)n ÷ ((1 + r)n − 1)
- M – monthly payment
- P – loan amount
- r – monthly interest rate = annual rate ÷ 12 (6% a year is 0.005 a month)
- n – number of payments = years × 12
For $10,000 at 6% over 5 years: r = 0.005 and n = 60, which gives a payment of $193.33.
An amortization schedule
Here is how the first months and the end of that loan look:
| Payment | Interest | Principal | Balance after |
|---|---|---|---|
| 1 | $50.00 | $143.33 | $9,856.67 |
| 2 | $49.28 | $144.05 | $9,712.62 |
| 3 | $48.56 | $144.77 | $9,567.85 |
| 12 | $41.92 | $151.41 | $8,231.95 |
| 30 | $27.69 | $165.64 | $5,373.31 |
| 60 | $0.96 | $192.37 | $0.00 |
Interest each month is the balance × 0.5%. Because the balance keeps falling, the interest share shrinks and the principal share grows, even though the payment never changes. (The last payment is adjusted by a few cents for rounding.)
What changes the total cost of a loan
- The interest rate. On a $20,000 five-year loan, 4% costs about $2,100 in interest while 12% costs about $6,700.
- The term. Stretching a $10,000 loan at 6% from 3 to 7 years lowers the payment from $304 to $146 but raises interest from about $950 to about $2,270.
- Fees. Origination fees and insurance are why the APR is usually higher than the advertised rate.
- Extra payments. Paying more than the minimum reduces the principal faster and cuts the interest.
How extra payments help
Any extra money you pay goes straight to the principal, so every future month is charged interest on a smaller balance. Even rounding the $193.33 payment up to $220 would clear the loan several months early and save interest. Check first that your lender allows early repayment without a penalty.
How much can you afford?
A common guideline is to keep all monthly debt payments below roughly a third of your take-home pay, and lower is safer. Work out your net income with the salary after tax calculator, then test different amounts and terms in the loan calculator until the payment fits comfortably, with room for savings and emergencies.
Checklist before signing
- Compare the APR from at least three lenders.
- Ask for the full amortization schedule.
- Read the rules on early repayment, late fees and insurance.
- Prefer the shortest term you can comfortably afford.
- Do not borrow for longer than the thing you are buying will last.
Try your own numbers in the loan repayment calculator. This guide is educational and is not financial advice.