Amortization Schedule

What Is an Amortization Schedule?

An amortization schedule is a complete table of periodic loan payments, showing the amount of principal and the amount of interest that comprise each payment until the loan is paid off at the end of its term. Each periodic payment is the same amount in total for each period. However, early in the schedule, the majority of each payment is what is owed in interest; later in the schedule, the majority of each payment covers the loan's principal. The last line of the schedule shows the borrower’s total interest and principal payments for the entire loan term.

Understanding an Amortization Schedule

In an amortization schedule, the percentage of each payment that goes toward interest diminishes a bit with each payment and the percentage that goes toward principal increases. Take, for example, an amortization schedule for a $250,000, 30-year fixed-rate mortgage with a 4.5% interest rate. The first few lines look like this:

Month 1

Month 2

Month 3

Total Payment

Principal Payment

Interest Payment

Interest to Date

Outstanding Loan Balance

$249,670.79

$249,340.34

$249,008.65

If you are looking to take out a loan, besides using an amortization schedule, you also can use a mortgage calculator to estimate your total mortgage costs based on your specific loan.

Formulas in an Amortization Schedule

Borrowers and lenders use amortization schedules for installment loans that have payoff dates that are known at the time the loan is taken out, such as a mortgage or a car loan. There are specific formulas that are used to develop an amortization schedule. These formulas may be built into the software you are using, or you may need to set up your amortization schedule from scratch.

If you know the term of a loan and the total periodic payment amount, there is an easy way to calculate an amortization schedule without resorting to the use of an online amortization schedule or calculator. The formula to calculate the monthly principal due on an amortized loan is as follows:

Principal Payment = Total Monthly Payment – [Outstanding Loan Balance x (Interest Rate / 12 Months)]

To illustrate, imagine a loan has a 30-year term, a 4.5% interest rate and a monthly payment of $1,266.71. Starting in month one, multiply the loan balance ($250,000) by the periodic interest rate. The periodic interest rate is one-twelfth of 4.5% (or 0.00375), so the resulting equation is $250,000 x 0.00375 = $937.50. The result is the first month's interest payment. Subtract that amount from the periodic payment ($1,266.71 - $937.50) to calculate the portion of the loan payment allocated to the principal of the loan's balance ($329.21).

To calculate the next month’s interest and principal payments, subtract the principal payment made in month one ($329.21) from the loan balance ($250,000) to get the new loan balance ($249,670.79), and then repeat the steps above to calculate which portion of the second payment is allocated to interest and which to principal. You can repeat these steps until you have created an amortization schedule for the full life of the loan.

Amortization tables typically include a line for scheduled payments, interest expenses, and principal repayment. If you are creating your own amortization schedule and plan to make any additional principal payments, you will need to add an extra line for this item to account for additional changes to the loan's outstanding balance.

How to calculate the total monthly payment

Typically, the total monthly payment is specified by your lender once you take out a loan. However, if you are attempting to estimate or compare monthly payments based on a given set of factors, such as loan amount and interest rate, you may need to calculate the monthly payment as well.

If you need to calculate the total monthly payment for any reason, the formula is as follows:

Total Monthly Payment = Loan Amount [ i (1+i) ^ n / ((1+i) ^ n) - 1) ]

Using the same example from above, we will calculate the monthly payment on a $250,000 loan with a 30-year term and a 4.5% interest rate. The equation gives us $250,000 [(0.00375 (1.00375) ^ 360) / ((1.00375) ^ 360) - 1) ] = $1,266.71. The result is the total monthly payment due on the loan, including both principal and interest charges.

Special Considerations

If a borrower chooses a shorter amortization period for their mortgage — for example, 15 years — they will save considerably on interest over the life of the loan, and they will own the house sooner. Also, interest rates on shorter-term loans are often at a discount compared to longer-term loans. Short amortization mortgages are good options for borrowers who can handle higher monthly payments without hardship; they still involve making 180 sequential payments (15 years x 12 months). It's important to consider whether or not you can maintain that level of payment.