How to Amortize a Loan

Suketu Mehta Mar 2, 2019
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Learn how to amortize a loan using a simple mathematical formula so that you can plan your loan repayment strategy well.
Amortization of a loan means dividing the it 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 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, 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 amount to be amortized over. To do this, multiply 12 to the number of years the money 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 subtract 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 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 amount (C).

Step 7

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

Step 8

Now, you will need to prepare the amortized schedule for making your payments. For this, you will have to equalize the new balance of the principal 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 can be  represented by a mathematical formula explained further.

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 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.
After calculating 'M' or the monthly payment amount using the  formula, you can use the formulae to arrive at your amortization schedule:
  • Monthly interest, H = J x P
  • Monthly principal payment, C = M - H
  • New principal 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. Various amortization calculators are also available online to help you out. You can do this in Excel using the formula given earlier. Just feed in the appropriate figures corresponding to their variables, and 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.
Disclaimer: This is for reference purposes only and does not directly recommend any specific financial course of action.