What a loan costs: monthly payment, total interest and extra payments

A loan's monthly payment is fixed by three numbers: the amount borrowed, the interest rate and the number of payments. Borrow 200,000 at 6% over 30 years and the payment is 1,199.10 a month. You pay about 431,676 in total, and about 231,676 of that is interest. The rest of this guide shows where those figures come from and how an extra payment changes them.

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The payment formula

Let P be the amount borrowed, r the monthly interest rate (the annual rate divided by 12, as a decimal) and n the number of monthly payments. The payment is:

M = P × r ÷ (1 − (1 + r)^−n)

For the example, r is 0.06 ÷ 12 = 0.005 and n is 30 × 12 = 360. The term (1.005)^−360 is about 0.16604, so the bottom of the fraction is 1 − 0.16604 = 0.83396. Then M = 200,000 × 0.005 ÷ 0.83396, which is 1,000 ÷ 0.83396 = 1,199.10.

With a rate of zero there is no interest, so the payment is simply P ÷ n. A loan of 1,200 over 12 months at 0% is 100 a month.

Total paid and total interest

Total paid is the payment times the number of payments: 1,199.10 × 360 is about 431,676. Total interest is the total paid minus the amount borrowed: 431,676 − 200,000 = 231,676. For this loan, about 54% of everything you pay goes on interest.

Why early payments are mostly interest

Interest each month is the balance owed times the monthly rate. In the first month the balance is 200,000, so the interest is 200,000 × 0.005 = 1,000. Of the 1,199.10 payment, only 199.10 reduces the debt. Each month the balance falls a little, the interest falls with it, and a larger share of the same payment goes to principal.

The effect is slow at first. After 180 payments, halfway through this loan, 142,097.69 is still owed. Only about 29% of the amount borrowed has been repaid, even though half the payments have been made.

Shorter terms cost less interest

The same loan over 15 years, at the same 6% rate, has a payment of 1,687.71. The total paid is 303,788.46 and the total interest is 103,788.46. The monthly payment is about 489 higher, and the interest is about 45% of the 30-year figure. The term is a trade between a monthly payment you can afford and the total cost. The percentage calculator is useful for comparing two totals like these.

Extra payments

An extra payment goes to the balance, so less interest builds up afterwards. On the 30-year loan:

• An extra 200 a month pays the loan off in 252 months, which is 21 years, and saves 108 months. The interest saved is 79,800.51.
• An extra 500 a month pays it off in 179 months, which is 14 years and 11 months, and saves 181 months. The interest saved is 129,141.83.

These figures assume the rate stays at 6%, the extra is paid every month from the start, and each extra payment reduces the balance straight away.

Some lenders treat an overpayment as an advance on future instalments rather than a cut to the balance. Ask how yours applies extra payments, and check the next statement to see that the balance went down.

What the figure leaves out

• Fees. Arrangement, valuation and closing fees are not in the payment.
• Insurance and taxes. Some mortgage payments include these and some do not. Check what the lender's quote covers.
• APR. The annual percentage rate includes some fees, so it is usually higher than the interest rate used here. Compare loans by APR, or by the total cost the lender shows.
• Variable rates. If the rate can change, the payment can change too. This calculator assumes a fixed rate.
• Rounding. This calculator uses the exact payment. Lenders round each payment to the cent and adjust the last one, so their totals can differ by a few cents.

Mortgages, car loans and personal loans

The formula is the same for all three. What differs is the term and the fees. Car loans are often shorter, and personal loans are often unsecured, which can change the rate. Rates vary by lender, country and borrower, so use the quote you were given rather than a typical figure.

Steps that work

1. Enter the amount borrowed, which is the price less any deposit.
2. Enter the annual rate exactly as quoted, and note whether it is an interest rate or an APR.
3. Enter the term in years or months.
4. Add an extra monthly payment to see how much time and interest it saves.
5. Compare the total interest across two or three terms before you choose.

Edge cases

• Interest-only loans. The balance does not fall during the interest-only period, so the formula above does not describe that part of the loan.
• Balloon payments. A large final payment changes the total, and this calculator does not model it.
• Long terms. The calculator stops at 100 years, which covers all common loans.

Quick answers

How is a monthly loan payment worked out? With the formula above: the amount times the monthly rate, divided by one minus one plus the rate raised to the negative number of payments.

Why is so much of the early payment interest? Because interest is charged on the balance, and the balance is largest at the start.

Does an extra payment really save money? Yes, by reducing the balance sooner, so less interest builds up. Check that the lender applies it to the principal.