How a loan payment is worked out
A standard loan is repaid in equal monthly payments. Each month the lender charges interest on what you still owe, and whatever is left of your payment reduces the balance. The payment that clears the loan in exactly n months is:
- payment = P × r × (1 + r)^n ÷ ((1 + r)^n − 1)
- P is the amount borrowed, r is the monthly rate (the yearly rate ÷ 12 ÷ 100) and n is the number of payments.
Borrow 250,000 at 6.5% a year for 30 years. The monthly rate is r = 6.5 ÷ 12 ÷ 100 = 0.0054167 and n = 360, so (1 + r)^360 is about 6.9918. The payment is 250,000 × 0.0054167 × 6.9918 ÷ 5.9918 = 1,580.17 a month. Over 360 payments that comes to about 568,862, so roughly 318,862 of it is interest, more than the 250,000 you borrowed.
At 0% there is no interest and the payment is simply the loan divided by the number of payments.
Why the early payments are mostly interest
Interest is charged on the balance, and at the start the balance is at its largest. In month 1 of the loan above, interest is 250,000 × 0.0054167 = 1,354.17, so only 226.00 of the 1,580.17 payment reduces the loan. About 86% of the first payment is interest. Because the balance falls slowly at first, the share of principal grows month by month and the last payments are almost all principal.
A shorter term costs more each month but far less overall. The same 250,000 at 6.5% over 15 years is 2,177.77 a month and about 141,998 of interest, against about 318,862 over 30 years.
The schedule under the answer shows this month by month. By year adds up each year's payments, principal and interest, and Every month lists each payment.
What extra payments do
An extra payment goes straight to the balance, so every later month's interest is worked out on a smaller number. Adding 200 a month to the loan above ends it after 265 payments, 22 years and 1 month instead of 30 years, and cuts the interest to about 221,243. That saves about 97,618 and 7 years 11 months. Small regular amounts matter more than they look because they start working on the first month.
Check two things with your lender before relying on this. Some loans charge a fee for repaying early, and some need you to say that the extra amount should go to principal rather than to the next payment.
What this calculator leaves out
- Fees. Arrangement fees, insurance and other charges are not in the payment. Many lenders quote an APR, which rolls some fees into a yearly rate. This calculator uses the plain interest rate.
- Different interest rules. Some lenders compound daily or every half year, or work out the first month's interest from the exact number of days. Your payment can differ by a little.
- Rates that change. A variable rate means the payment is recalculated later. Work out each new rate as a fresh loan with the balance that remains.
- Other payment schedules. Payments are monthly. Weekly and fortnightly plans are not worked out here.
- Rounding. The payment and each month's interest are rounded to the cent, as a statement shows them, and the last payment clears whatever is left. It can differ from the others by a small amount.