Loan amortization calculator

How is a loan payment calculated?

Almost every installment loan, from a mortgage to an equipment loan, is repaid in equal payments: the same amount every month, from the first payment to the last. That amount depends on three inputs: the amount borrowed, the interest rate and the term.

• Payment = loan amount × r ÷ (1 − (1 + r)⁻ⁿ), where r = annual rate ÷ payments per year, and n = total number of payments.
• Interest in a payment = remaining balance × r.
• Principal repaid = payment − interest.
• Total cost of the loan = payment × n − loan amount, plus insurance.

The calculator divides the annual rate by the number of payments per year (6% a year gives 0.5% a month), the usual convention for fixed-rate mortgages and installment loans. You can check it by hand: $100,000 × 0.005 ÷ (1 − 1.005⁻³⁶⁰) = $599.55.

How to read an amortization schedule

Each line is one payment. It shows what you pay, how much goes to interest, how much actually pays down the debt, and what you still owe. For $100,000 at 6% over 30 years, the payment is $599.55. The first one contains $500 of interest and only $99.55 of principal; the last one is almost all principal.

After one year, the borrower has paid $7,194.61, of which $5,966.59 was interest, and still owes $98,771.99. Half of the principal is only repaid after 252 payments, 21 years in. That is why an extra payment early in the loan saves far more interest than the same payment near the end, and why selling a home financed with a long loan after a few years leaves little equity built through payments.

Term, rate, insurance: what drives the cost of a loan

Loan	Payment	Interest	Total cost
$100,000 at 6% over 15 years	$843.86 a month	$51,894.23	$51,894.23
$100,000 at 6% over 20 years	$716.43 a month	$71,943.45	$71,943.45
$100,000 at 6% over 30 years	$599.55 a month	$115,838.19	$115,838.19
$300,000 at 6.5% over 30 years	$1,896.20 a month	$382,633.47	$382,633.47
$30,000 at 7% over 5 years, insurance 0.5%	$594.04 + $12.50 of insurance	$5,642.16	$6,392.16

Stretching $100,000 from 15 to 30 years lowers the payment by $244.31 a month but adds $63,943.96 of interest. Insurance here is charged on the original loan amount, as mortgage insurance (PMI) usually is on a conventional mortgage with a small down payment. The calculator spreads it evenly over the whole term, while PMI can often be cancelled once you have enough equity, so treat that line as an upper bound.

Business loans: what the lender looks at

For a business, the whole payment leaves the bank account every month, but only the interest is an expense on the income statement: the principal repaid does not reduce profit. A profitable small business can therefore run short of cash if its loan payments exceed the cash its operations generate.

That is why lenders compare annual loan payments with the cash flow the business produces, often as a debt service coverage ratio: cash flow available for debt service ÷ annual debt payments. A ratio comfortably above 1 means the business can pay its loans out of its operations. To see how much revenue your costs, loan payments included, require, run the numbers through the break-even calculator.

What an amortization schedule doesn't show

• Upfront costs: origination fees, points, closing costs. They are part of the APR, not of the schedule.
• Prepayment penalties, if the loan agreement includes any.
• Rate changes on an adjustable-rate loan, for which a schedule is only a projection.

To check an offer, compare the lender's schedule with this one using the same interest rate and term: the payments should match to the cent, insurance aside.