Lenders use a method called amortization, which is the spreading out of fixed loan payments over time, to calculate interest on a mortgage loan. If you have a fixed-rate mortgage, amortization will produce the same monthly payments over the life of the loan. A variable-rate mortgage will produce a new monthly payment amount each time the interest rate changes.

In either case, each fixed monthly payment, known as the equated monthly installment, is uniquely split between interest charges and the repayment of principal, according to an amortization schedule.

## The Amortization Schedule

An amortization schedule heavily favors interest during the early years, but eventually, principal predominates later in the loan term. If you like math, you can use a formula to figure your first-month interest payment and a spreadsheet to produce the full amortization schedule showing how much interest you’ll pay each month. However, its much simpler to use an online mortgage calculator, available on a number of websites.

## How Amortization Works

Assume you have a 5-percent fixed rate, 30-year mortgage on a $300,000 house on which you put down $60,000 and borrow $240,000. Ignoring other factors like property tax or HOA fees, the fixed monthly payment is calculated using this formula:

M = P*r(1+r)^n/(1+r)^n – 1

where M is the monthly payment, P is the principal borrowed amount, r is the one-month interest rate (i.e., the annual interest rate divided by 12) and n is the number of monthly payments. The caret (^) indicates exponentiation. In the example, the monthly interest rate is 0.05 / 12, or 0.004167. Plugging in the variables produces:

M = ($240,000) * 0.004167(1+0.004167)^360/(1+0.004167)^360 – 1

M = $1,288.37

If you prefer, you can use the Excel spreadsheet PMT function and plug in the monthly interest rate, number of months and the initial value (the principal amount). In this case, enter:

=PMT(0.004167,360,240000)

The result is $1,288.37.

M or the monthly payment remains the same over the entire 360-month term. What varies is how much interest you pay each month. You can construct a spreadsheet to find the interest/principal split for each month.

## Constructing an Amortization Schedule

In your favorite spreadsheet program, you’ll create the following 6-column, 360-row spreadsheet based on the example. The columns are:

A. **Month number**, with rows numbered from 1 through 360.

B. **Start balance**, with $240,000 entered into the first row and subsequent rows set equal to the previous row’s end balance.

C. **Payment**, which is fixed at $1288.37 for each row.

D. **Interest**, equal to the row’s start balance times the monthly interest rate of 0.004167.

E. **Principal**, which is the row’s start balance minus the interest amount.

F. **End balance**, equal to the row’s start balance minus the principal amount.

The total interest you’ll pay on the mortgage, assuming no prepayments or late payments, is the sum of Column D, Interest, which in the example is $223,813.88.

## Using a House Payment Calculator

You can avoid all the math by using on online house payment calculator such as the Bankrate mortgage calculator. Simply enter the home price, the down payment, the length of the loan and the annual interest rate. The calculator returns the estimated monthly payment. Entering the example data of a $300,000 home price, a $60,000 down-payment, a 30-year loan term and a 5-percent interest rate, the calculator returns a monthly payment of $1,288 and a total interest amount of $223,990, which differs slightly from the spreadsheet results due to rounding.

As an additional benefit, the calculator offers extra features that help you figure your total monthly payments by factoring in items like property tax, homeowner’s insurance and HOA fees. These additional costs do not affect the total interest you will pay on the loan.

### Tip

- Annual percentage rate is usually given as a percent, such as 4.5 percent, and must be converted to a decimal, such as 0.045, for use in these calculations.

### References

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