# How to calculate for the amortization factor

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In my previous post: How to compute for the monthly amortization payment without a mortgage calculator,  I showed how I compute for the monthly amortization payment by hand. Tyrone of  Millionaire Acts through his comment asked: “How about if we don’t have access to the amortization factors table? Is there a way to compute it?”. I answered yes in my own comment and I would like to illustrate how it can be done through this post.

I got the following amortization factor formula when I reviewed for the November 2007 Real Estate Brokers Licensure Exam under Engineer Enrico Cruz:

I

Amortization Factor = ———————————–

-M

1 – ( 1 + I )

Where:

I = the monthly interest rate. You can easily get this by dividing the annual interest rate by 12

M = the loan payment term in months. Just multiply the loan term by 12.

Let us use the same example in my previous post.
A foreclosed property is being sold for Php 1 Million and you can purchase it with only 20% down payment, with a maximum payment term of 10 years, at an annual interest rate of 12%. What would be the amortization factor you will use to compute for the monthly amortization?

First, let us compute for the Monthly Interest Rate (I) and the Loan payment term in Months (M)

= 12%/12
= 1%

### M = 10 years x 12 months/year

= 120 months

1%

Amortization Factor = ———————————–

-120

1 – ( 1 + 1% )

0.01

= ———————————–

-120

1 – ( 1+0.01 )

= 0.01434709

As you can see, we arrive at the same value for the amortization factor we used in my previous example. Of course I would only use the formula in excel as I would not want to compute this by hand, it would be very difficult to calculate for a number with a negative exponent like that in the example  right?!

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I would still prefer to keep a copy of the amortization factor table in my wallet so I don’t need to bring my laptop with me everywhere. I can then compute by hand or use the calculator on my cellphone. By the way, I believe there is also a built-in function in excel that can do this calculation but I haven’t tried it yet.

Easy right?!

To our financial freedom!

Jay Castillo
Real Estate Investor
Real Estate Broker License #: 20056
Blog: http://www.foreclosurephilippines.com
Click here to contact me via E-mail
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Text by Jay Castillo. Copyright © 2009 All rights reserved.

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About Jay Castillo

Jay is the founder of Foreclosurephilippines.com where he shares real estate investing tips and foreclosed property listings. He was an I.T. Manager that loved to make things work, which is exactly what he did when he crossed-over to Real Estate Investing and Internet Marketing. He is also a licensed real estate broker with PRC License # 3194 ... [Continue reading]

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• http://www.foreclosurephilippines.com Jay Castillo

Hi Jaelin, will create a table for this when I have time, or I’ll just create a calculator that illustrates this.

• Cynthia

What about if monthly interest is applied on diminishing balance?

• http://www.foreclosurephilippines.com Jay Castillo

Hi Cynthia, the formula above is already for what you said. Thanks.

• Gigi

Hi Jay. how do you derive the factor using the scientific calculator? thanks

• http://www.foreclosurephilippines.com Jay Castillo

Hi Gigi, please see link to wikipedia in my answer to Thales for the same question. Thanks.

• thales

hi jay,

how did they derive this formula? thanks..

• Gil B.

Hi Jay,
I appreciate very much the knowledge you’re sharing. I just want to find out how to do the formula you gave (the one with a negative exponent) on Excel. Thanks so much.

• http://www.foreclosurephilippines.com Jay Castillo

Hi Gil, to enter a negative exponent in excel, you can use ^-X where X is the exponent. You can also download this file to see an example: http://www.foreclosurephilippines.com/wp-content/uploads/2009/09/amortization_table(Unionbank).xls

By the way, you can also use the PMT function in Excel:
PMT function: Calculates the payment for a loan based on constant payments and a constant interest rate.

Syntax

PMT(rate,nper,pv,fv,type)

For a more complete description of the arguments in PMT, see the PV function.

Rate is the interest rate for the loan.

Nper is the total number of payments for the loan.

Pv is the present value, or the total amount that a series of future payments is worth now; also known as the principal.

Fv is the future value, or a cash balance you want to attain after the last payment is made. If fv is omitted, it is assumed to be 0 (zero), that is, the future value of a loan is 0.

Type is the number 0 (zero) or 1 and indicates when payments are due.

Set type equal to If payments are due
0 or omitted At the end of the period
1 At the beginning of the period

Remarks:
The payment returned by PMT includes principal and interest but no taxes, reserve payments, or fees sometimes associated with loans.
Make sure that you are consistent about the units you use for specifying rate and nper. If you make monthly payments on a four-year loan at an annual interest rate of 12 percent, use 12%/12 for rate and 4*12 for nper. If you make annual payments on the same loan, use 12 percent for rate and 4 for nper.
Tip To find the total amount paid over the duration of the loan, multiply the returned PMT value by nper.

• mildred

you are so helpful and selfless! thanks for putting up this blog

• http://www.foreclosurephilippines.com Jay Castillo

Thanks Mildred, I really appreciate your kind words!