How to Amortize a Loan

Amortization of a loan means dividing the loan amount in such a way, that you make equal payments of the interest as well as principal amount of any pending loan. It is basically a monthly structure following which the borrower pays back the loan amount along with interest to the lender. Learning how to amortize a loan will help you make more payments towards your principal amount to finish it off early so that you are liable to pay only interest amount later. It helps you in preparing an effective pay-back strategy which suits your financial position.

Amortization Calculations

Step 1
To begin with, convert the monthly installments you are paying in a decimal format. To do this, divide your monthly interest by 1200, and the mark the figure you arrive at as J. You will require this for further calculations, so note it down.

Step 2
You will then have to calculate for how many months you want your loan to be amortized over. To do this, multiply 12 to the number of years the loan is spread over (N). You will require this value for further calculations so note it down.

Step 3
Now you will need to figure out the denominator for your monthly payment amount. For this, add 1 to the value you got in the first step (J). Raise the (J + 1) figure to the negative N power (-N), and minus it from 1. This is your denominator.

Step 4
After the above step when you have your denominator, divide the value from Step 1 (J) by it. This whole thing needs to be multiplied with your loan's principal amount (the initial amount). The quotient you arrive at is your monthly payment amount.

Step 5
The monthly interest at present (H) can be calculated by multiplying the principal amount (P) with your monthly interest which you have converted to decimals (J).

Step 6
When you subtract the amount you got in the previous step (H) from your monthly payment amount (M), it will give you the amount you will pay each month towards your principal loan amount (C).

Step 7
The new balance of the principal loan can be obtained by reducing your monthly principal payment amount (C) from the principal loan amount (P).

Step 8
Now you will need to prepare the amortized loan schedule for making your payments. For this, you will have to equalize the new balance of the principal loan amount (Q), to the initial principal amount (P). Then follow steps 5, 6 and 7 again and again till you get the value as 0 (zero).

Amortization Formula

The steps mentioned above can be easily represented in the way of a mathematical formula. This formula is given below:

M = P x	J
	1 - (1 + J) ^ - N

In this formula, the meaning of letters (variables) used are:

• J : It is the monthly interest payable in decimal form. Divide your interest amount by 1200.
• P : This is the initial amount of loan known as the principal amount.
• L : It denotes the length or period over which the loan is amortized. It is in years.
• N : This is the length of the loan in terms of months. Multiply L with 12 to get this value.
• I : It is the yearly interest rate and is expressed in percentage.
• M : The monthly payment you need to make to amortize the loan.

After you have calculated 'M' or the monthly payment amount using the above formula, you can use the formulae listed below to arrive at your amortization schedule:

• Monthly interest, H = J x P
• Monthly principal payment, C = M - H
• New principal loan balance, Q = P - C
• Make P = Q and start again from 1, till both values come down to 0 (zero).

This will give you your amortization schedule.

After learning about amortizing a loan, use it to your benefit. Yet you may ask 'how do you amortize a loan' without all this seemingly difficult math. Various loan amortization calculators are also available online to help you out. Also, you can amortize a loan in Excel using the formula given earlier. Just feed in the appropriate figures corresponding to their variables, and simply feed in the formula in the excel sheet to arrive at the amortization schedule. You will need very good knowledge and an excellent command over Microsoft Excel to use it. Be careful while feeding figures as even a tiny blunder could result in the whole amortization schedule going for a toss.