How Loan Payments Are Calculated: Amortization Explained With a Worked Example

You borrow 200,000, the bank quotes 6% over 20 years, and a payment of about 1,433 a month appears. Where does that number come from, and why does it feel as though the balance hardly moves in the first few years? This guide opens the black box. You will see the formula, a worked example, what the amortization schedule shows, and how extra payments change the picture. You can try your own figures in the loan installment calculator or the mortgage calculator.

The three inputs

Every standard fixed-rate loan is defined by:

• Principal (P): the amount you borrow.
• Interest rate: usually quoted per year, but charged per month. The monthly rate (r) is the annual rate divided by 12.
• Term (n): the number of monthly payments.

The payment formula

For a loan repaid in equal monthly installments, the payment is:

Payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)

It looks heavy, but it simply finds the fixed payment that pays off the principal and all the interest over n months, so that the balance reaches exactly zero at the end.

A worked example

Borrow 200,000 at 6% a year for 20 years (240 months).

• Monthly rate r = 0.06 ÷ 12 = 0.005
• n = 240
• (1.005)^240 ≈ 3.3102

Payment = 200,000 × 0.005 × 3.3102 ÷ (3.3102 − 1) = 1,000 × 3.3102 ÷ 2.3102 ≈ 1,432.86 a month.

Over 240 payments you repay 1,432.86 × 240 ≈ 343,887. Subtract the 200,000 you borrowed, and the interest cost is about 143,887, nearly three quarters of the amount borrowed.

What the amortization schedule shows

An amortization schedule splits each payment into interest and principal. Using the same loan:

Month 1. Interest = 200,000 × 0.005 = 1,000. The rest of the payment, 1,432.86 − 1,000 = 432.86, reduces the principal. New balance: 199,567.14.

Month 2. Interest = 199,567.14 × 0.005 = 997.84. Principal repaid = 435.02. Balance: 199,132.12.

Each month the interest charge shrinks slightly, so a little more of the fixed payment goes to principal. The shift is slow at first, which is why early years feel like running on the spot. In the last few years the picture flips: most of each payment reduces principal and only a sliver is interest.

Why does this matter? If you sell or refinance early, you will have repaid far less of the principal than you might expect. After five years on this loan, you have paid 85,972 in total but still owe about 169,800.

Shorter term: higher payment, far less interest

Keep the same 200,000 at 6% but choose 15 years instead of 20.

• Payment ≈ 1,687.71 a month (about 255 more).
• Total interest ≈ 103,788, compared with 143,887 over 20 years.

You pay around 40,000 less in interest, in exchange for about 255 more a month. A shorter term is the biggest single lever on total cost, but only if the higher payment fits your budget comfortably.

Extra payments: how they work

An extra payment reduces the principal directly. A smaller principal means less interest every month after that, so the saving compounds.

Add 100 a month to the 20-year loan above, applied to principal:

• The loan is repaid in about 212 months (roughly 17 years and 8 months) instead of 240, saving about 28 months.
• Total interest falls to about 124,743, saving around 19,144.

For 100 a month over 17 years, that is a good return. The earlier in the loan an extra payment is made, the more interest it avoids. Before overpaying, check whether your lender allows it without a penalty, and whether extra payments shorten the term or reduce the monthly amount. Also compare the guaranteed saving against what that money might earn elsewhere or whether you have higher-rate debt to clear first.

Fixed payment versus fixed principal

The example above uses the common "annuity" structure, with a constant payment. Some countries and products use a different structure where the principal portion is constant and the payment starts higher and falls over time. In Brazil these are the Price and SAC systems. SAC costs less interest overall; Price has a lower first payment. If you are comparing them, see SAC or Price: which financing compensates more or the Brazil SAC and Price simulator (in Portuguese).

What the payment does not include

The calculated payment covers principal and interest only. A real loan can add:

• Fees such as arrangement, valuation or administration costs.
• Insurance, often required for mortgages.
• Taxes, for example property tax paid with a mortgage.
• Variable rates, where the payment changes when the rate does.

Compare offers using the total amount you will repay and the lender's annual percentage rate (APR), where your country requires it, not just the monthly figure.

How to use this when you borrow

1. Decide the payment you can afford comfortably, not the maximum the lender will give you.
2. Compare two or three terms side by side, looking at both the payment and the total interest.
3. Ask whether extra payments are allowed without a fee.
4. Check the full cost, including fees and insurance.
5. Keep a buffer. A payment that fits only when nothing goes wrong is too high.

Quick answers

Why is the payment the same every month if the interest changes? Because the formula is built so that interest plus principal always add to the same total. As the interest part falls, the principal part rises.

Does a bigger deposit help? Yes. It reduces P, which reduces the payment, the total interest and often the rate you are offered.

Is paying every two weeks better? Paying half the monthly amount every two weeks results in 26 half-payments, equal to 13 monthly payments a year, so you overpay one month a year. The effect is the same as a small extra payment.

The mathematics of a loan is not mysterious. Once you know that interest is charged on the balance, and that the balance falls slowly at first, most of the advice on borrowing follows: borrow less, borrow for less time if you can, and overpay early if it makes sense.

This article is general information and an illustration of the arithmetic, not financial advice. Check your own loan agreement for the exact terms.