Amortization Formula: How Monthly Mortgage and Loan Payments Are Calculated
The formula behind every fixed-rate mortgage — explained step by step, with an interest/principal breakdown, the effect of overpayments, and a comparison with interest-only loans.
The Monthly Payment Formula
A fixed-rate repayment mortgage (or any fully amortizing loan) uses a single formula to calculate the monthly payment that will pay off the entire debt — principal and interest — over an agreed term. Each monthly payment is identical, but the split between interest and principal changes every month.
Variable definitions:
- M — fixed monthly payment
- P — principal (total loan amount)
- r — monthly interest rate (annual rate ÷ 12, as a decimal)
- n — total number of monthly payments (years × 12)
Step-by-Step Worked Example
A £200,000 mortgage at 4.5% annual interest over a 20-year term.
Step 1: Monthly rate → r = 0.045 ÷ 12 = 0.00375
Step 2: Total payments → n = 20 × 12 = 240
Step 3: Compounding factor → (1 + 0.00375)240 = (1.00375)240 = 2.4557
Step 4: Numerator → 0.00375 × 2.4557 = 0.009209
Step 5: Denominator → 2.4557 − 1 = 1.4557
Step 6: Ratio → 0.009209 ÷ 1.4557 = 0.006326
Step 7: Monthly payment → M = 200,000 × 0.006326 = £1,265/month
240 payments of £1,265 = £303,600 total paid · Interest = £103,600
How an Amortization Schedule Works
Although the monthly payment stays constant at £1,265, the proportion that goes to interest versus principal shifts every month. In the early years, most of each payment covers interest. In the final years, almost all of it reduces the principal. This is called front-loading.
Month 1 breakdown:
Interest: £200,000 × 0.00375 = £750.00
Principal: £1,265 − £750 = £515.00
Remaining balance after month 1: £200,000 − £515 = £199,485
The table below shows how the interest/principal split evolves across the 20-year term:
| Year | Month | Approx. balance | Monthly interest | Monthly principal |
|---|---|---|---|---|
| 1 | 1 | £200,000 | £750 | £515 |
| 5 | 61 | ~£165,400 | ~£620 | ~£645 |
| 10 | 121 | ~£122,100 | ~£458 | ~£807 |
| 15 | 181 | ~£67,900 | ~£255 | ~£1,010 |
| 20 | 238 | ~£2,500 | < £10 | ~£1,255 |
The Effect of Extra Payments
Any payment above the required monthly minimum reduces the outstanding principal directly — reducing the balance on which future interest is calculated. This creates a compounding benefit: lower balance → less interest → more of the next payment reduces principal → even lower balance.
On the £200,000 example above, paying an extra £200/month (total payment: £1,465) reduces the term by approximately 4 years — the mortgage is paid off in around 16 years instead of 20 — and saves roughly £22,000 in total interest. The earlier you start overpaying, the greater the saving, because the benefit compounds over the remaining term.
Use the Mortgage Payoff calculator to see the exact impact of a specific overpayment amount on your own mortgage.
Amortization vs Interest-Only Loans
An interest-only loan charges only the interest each month: M = P × r. No principal is repaid during the term. For the same £200,000 at 4.5%, the monthly payment is just £200,000 × 0.00375 = £750/month — significantly lower than the £1,265 repayment payment.
However, the full £200,000 principal remains outstanding and must be repaid in a lump sum at the end of the term. Over 20 years: total interest paid = 240 × £750 = £180,000, plus £200,000 principal repayment = £380,000 total, compared to £303,600 for the repayment mortgage. Interest-only costs £76,400 more in this example, and carries the risk of not having funds to repay the principal at term end.
Use the free mortgage calculator — enter your loan amount, rate, and term to get the monthly payment, full amortization schedule, and total interest paid.
Open Mortgage Calculator →Frequently Asked Questions
What does amortization mean?
Amortization describes paying off a debt through regular equal payments over a fixed period. Each payment covers the month's interest first; the remainder reduces the principal. Over time the interest portion shrinks and the principal portion grows, even though the total monthly payment stays constant.
Why do I pay more interest at the start?
Interest is calculated on the outstanding balance, which is highest at the beginning. In month 1 of a £200,000 mortgage at 4.5%, £750 of the £1,265 payment is interest. As the balance falls over subsequent years, the interest charge shrinks — this front-loading is a mathematical consequence of the formula, not a lender choice.
How does the interest rate affect my monthly payment?
Significantly. On a £200,000, 20-year mortgage: 3.5% → ~£1,160/month, 4.5% → ~£1,265/month, 5.5% → ~£1,376/month. The difference between 3.5% and 5.5% is £216/month and over £36,000 in total interest across the full term.
What happens if I make extra payments?
Extra payments reduce the principal directly, so less interest accrues in following months, shortening the term. On the £200,000 example, an extra £200/month saves roughly £22,000 in interest and pays off the mortgage 4 years early. Use the Mortgage Payoff calculator to see the exact impact for your situation.
Evidence & Methodology
How This Page Is Grounded
Method
Derives the level-payment loan equation and shows how each payment is divided between interest and principal.
Important limitation: The derivation assumes a fixed periodic rate, regular payments and no fees or irregular day-count convention.
Primary Sources
- How mortgage amortization works Consumer Financial Protection Bureau
Quality Checks
Worked examples are checked against a full month-by-month balance schedule.
See how sources are selected and corrections are handled in our Editorial & Calculation Methodology, and which automated checks this page has to pass in How We Test.