Understanding Loan EMI Calculation as a Monthly SIP Investment!

A simple way to understand a loan EMI calculation in terms of a lump sum investment and a monthly SIP is discussed in this post.  This is applicable for all kinds of loans – home loan, car loan, personal loan etc.

There is a close connection between investment mathematics and loan/mortgage mathematics. In fact, those familiar with the formulae would tell you that they are pretty much identical!

Here is how a home loan EMI can be understood in terms of a lump sum and monthly SIP investment.

Suppose we want a loan of Rs. 10, 00,000  (10L) from a bank at annual interest rate of 10%. This is how the bank will calculate the equated monthly installment or the EMI.

16770232616_f5ac8b1594_z
Photo credit: Got Credit

You want 10L from the bank. Instead of giving this money to you, if the bank had invested it at the rate of 10% a year for 30 years, it would get

1000000 x(1+ 10%/12)^360 =  19837399.4 (198.37 Lakhs)

Here 10%/12 is the monthly interest rate and 360 = duration in months (30 x 12).

If the bank has to lend 10L to you, its aim would be to receive 198.37L from you over 30 years at the same rate of interest, payable each month.

You will not be paying 198.37L to the bank, but you will be paying a monthly amount, which if invested at the same rate would fetch the bank 198.37L after 30 years.

Therefore, as far as the bank is concerned the EMI is a monthly SIP received from you for 30 years, calculated in the following way:

What amount should you invest each month at the rate of 10% a year, so that after 30 years, the investment value is 198.37L? Ring a bell?

This question would be familiar to anyone who has used financial goal calculator. This is the calculation:

19837399.4 = SIP x [(1+10%/12)^360-1]/(10%/12)

This is inverted to calculate the SIP = 877.5.7 ~ 8776.

Therefore, the bank sets the EMI as 8776.

The loan EMI calculation is derived in the following way:

19837399.4 = EMI x [(1+10%/12)^360-1]/(10%/12)

1000000 x(1+ 10%/12)^360 = EMI x [(1+10%/12)^360-1]/(10%/12)

Thus the loan calculation can be viewed as an investment equation:

Lump sum investment value = SIPinvestment value

Now, 1000000 = P = loan amount

10%/12 = R = interest rate per month

360 = n = duration in months

So we have, P x(1+ R)^n = EMI x [(1+R)^n-1]/R

Therefore, EMI =P x R x(1+ R)^n / [(1+R)^n-1]

Credit: This post is based on my answer in Facebook Group Asan Ideas for Wealth.

Want to conduct a sales-free "basics of money management" session in your office?
I conduct free seminars to employees or societies. Only the very basics and getting-started steps are discussed (no scary math):For example: How to define financial goals, how to save tax with a clear goal in mind; How to use a credit card for maximum benefit; When to buy a house; How to start investing; how to invest for and after retirement etc. depending on the audience. If you are interested, you can contact me: freefincal [at] Gmail [dot] com. You need to only cover my travel fare for the session.

Connect with us on social media


Do check out my books


You Can Be Rich Too with Goal-Based InvestingYou can be rich 243x300 - Understanding Loan EMI Calculation as a Monthly SIP Investment!

My first book is now available at a 35% discount for Rs. 258. It comes with nine online calculators. Get it now.  The Kindle edition is only Rs. 199.

Gamechanger: Forget Startups, Join Corporate & Still Live the Rich Life You Want

Cover pink - Understanding Loan EMI Calculation as a Monthly SIP Investment! My second book is now only Rs 199 (Kindle Rs. 99) Get it or gift it to a young earner

The ultimate guide to travel by Pranav Surya

Travel-Training-Kit-Cover This is a deep dive analysis into vacation planning, finding cheap flights, budget accommodation, what to do when travelling, how travelling slowly is better financially and psychologically with links to the web pages and hand-holding at every step.  Get the pdf for ₹199 (instant download)

Create a "from start to finish" financial plan with this free robo advisory software template


Free Apps for your Android Phone

All calculators from our book, “You can be Rich Too” are now available on Google Play!
Install Financial Freedom App! (Google Play Store)
Install Freefincal Retirement Planner App! (Google Play Store)
Find out if you have enough to say "FU" to your employer (Google Play Store)

About Freefincal

Freefincal has open-source, comprehensive Excel spreadsheets, tools, analysis and unbiased, conflict of interest-free commentary on different aspects of personal finance and investing. If you find the content useful, please consider supporting us by (1) sharing our articles and (2) disabling ad-blockers for our site if you are using one. We do not accept sponsored posts, links or guest posts request from content writers and agencies.

Blog Comment Policy

Your thoughts are vital to the health of this blog and are the driving force behind the analysis and calculators that you see here. We welcome criticism and differing opinions. I will do my very best to respond to all comments asap. Please do not include hyperlinks or email ids in the comment body. Such comments will be moderated and I reserve the right to delete the entire comment or remove the links before approving them.

6 thoughts on “Understanding Loan EMI Calculation as a Monthly SIP Investment!

    1. I never said that. I recommend taking a home loan once finances are a bit stabilized and at least 10-15% can be invested each month even after paying EMI.

      1. Yeah, it is very difficult thing to handle.. people usually stretch themselves for the EMI.Currently I am in same dilemma

  1. Sir, great article. Nothing can be understood more clearly than mathematics. However I found a catch in above formula. Home loan formula implicitly assumes that compounding frequency is monthly. Also SIP formula is for month end SIP. More importantly in SIP formula monthly rate of return is determined by(1+CAGR)^(1/12)-1 while banks simply divides the annual rate by 12 to arrive at monthly return. Please correct me if I wrong. Thank you.

Leave a Reply

Your email address will not be published. Required fields are marked *