Amortization Calculator

The formula

M = P × [ r(1 + r)ⁿ ] ÷ [ (1 + r)ⁿ − 1 ]

Beginning with the first month's payment (M), we are going to use this monthly amount for all future months. The first month's payment is applied as follows; the interest due on the loan is the existing loan value (P) times the monthly rate (r). That leaves a remainder which will be used to pay down some or all of the loan balance. This process continues each subsequent month using the new total loan value as the basis for calculating the interest and again paying down the loan balance until it reaches zero.

Worked example, using the default $340,000 at 6.67% over 30 years. The payment is $2,187. In the very first month, $1,890 of that is interest and only $297 touches the balance. Carry it to term and you pay $447,386 in interest, which is 132% of the loan again on top of repaying it.

Mortgage amortization

A mortgage is where amortization does its most extreme work, because 360 payments is long enough for the front-loading to get genuinely lopsided. Take a $300,000 loan at 6.5% over 30 years. The required payment is $1,896 a month. In month one, $1,625 of that is interest and only $271 goes to the balance, so 14% of your first payment is actually buying the house.

It stays lopsided for a long time. Principal does not overtake interest until month 233, which is year 19 of 30. For the first two-thirds of a standard mortgage you are paying the lender more than you are paying yourself, which is why the schedule is worth reading before you decide how long a term to take.

Two things a mortgage amortization schedule deliberately leaves out: property taxes and homeowners insurance. Those usually arrive in the same monthly bill through escrow, but they do not amortize and extra payments do not reduce them, so including them would only make the principal and interest split harder to read.

Why the early payments feel like they do nothing

This is the section of the question that causes the confusion for many applicants and there is no hidden element in this. Your debt accumulates interest from the moment you borrow it. You have the highest amount borrowed (the highest) at the start; therefore the interest component will be the largest as well. However, your payments are constant so when the outstanding amount decreases, the interest decreases too, and since you pay a fixed sum each month, the interest piece becomes smaller and the interest is replaced by the principal portion. The time at which more of your monthly repayments go toward paying off the original debt rather than just paying interest is later than you might expect on longer term loans.

Switch the table to the monthly view and you can watch it happen row by row. It also explains why refinancing or moving resets the clock: a new loan puts you back at the interest-heavy end of the schedule, even if the rate is better.

What an extra payment really buys

Put anything in the "extra" field, and the summary will show both (1) the money saved by reducing the number of payments and (2) the number of months you save by paying now. The second comes from the first. Any money paid toward principal reduces the total future interest on that portion of the loan. As such, a larger principal reduction at the beginning of a mortgage saves substantially more money than if it were made later. This asymmetry is the most important lesson to be learned using an amortization table.

If it's a mortgage you already hold and you want to model this properly across several loans, the mortgage payoff calculator is built for exactly that. If you're still pricing a house, start with the mortgage calculator, which works back from purchase price and adds tax, insurance and PMI.

Reading the amortization schedule

The amortization schedule is the table itself. Each row in the table represents a payment made on an amortizing loan. For each row, the table provides information about the first four questions listed above (the amount of the interest portion of that particular payment, the amount of that particular payment applied toward reducing the outstanding principal balance, if there was any excess payment made, and how much would remain after that particular payment).

As you scan down the "Interest" column of the table, you will see the value of interest being lessened with each subsequent row. As you scan down the "Principal Paid" column of the table, you will see the value of the principal remaining as a liability decreasing. At no time will the total of the values in both columns exceed your fixed monthly payment. That is precisely the purpose of an amortizing loan: to allow for the amount of the payments to be fixed, while allowing the proportion of those payments to go toward interest vs. principal to vary.

Printing this schedule allows you to quickly compare what your lender stated in their monthly statements (lender's statements) with the row on this table corresponding to each month. This is the quickest way to find out if there has been a misapplied payment by comparing each lender's monthly statement. It also will show you at what month an additional payment would be taken off of the end of your loan.

What this leaves out

Fees are not modelled. Origination charges, closing costs and any prepayment penalty sit outside the schedule, and a prepayment penalty in particular can undo the case for extra payments entirely, so check your loan agreement before acting on the savings figure. Interest that compounds daily rather than monthly will differ slightly from these rows. And the auto, student and personal rates here are placeholders, not market data.