Every home loan calculator, including ours, uses the same formula. You do not need to remember it. Knowing how it works shows why a small change in rate or tenure moves your EMI so much.
What is an EMI?
EMI stands for equated monthly instalment. It is the fixed amount you pay your bank on the same date every month until the loan is cleared. "Equated" means the amount stays the same even though the mix inside it keeps changing. Early on, most of your EMI pays interest. Later, most of it repays the loan itself.
The formula
EMI = P x r x (1 + r)^n / ((1 + r)^n - 1)
There are only three inputs.
- P is the principal, the amount you borrow.
- r is the monthly interest rate. Take the yearly rate, divide by 12, then divide by 100. A rate of 8.5% a year becomes 8.5 / 12 / 100 = 0.0070833.
- n is the number of monthly instalments. A 20-year loan has 20 x 12 = 240 of them.
The part (1 + r)^n is the compounding factor. It tells you how much a rupee of debt grows over the whole tenure if you never paid anything. The formula then finds the equal monthly payment that brings the balance to exactly zero at month n.
A worked example
Say you borrow 50 lakh (P = 5,000,000) at 8.5% for 20 years.
- Monthly rate: r = 8.5 / 12 / 100 = 0.0070833.
- Instalments: n = 240.
- Compounding factor: (1.0070833)^240 = 5.4412.
- Top of the formula: 5,000,000 x 0.0070833 x 5.4412 = 192,711.
- Bottom of the formula: 5.4412 - 1 = 4.4412.
- EMI = 192,711 / 4.4412 = about 43,391.
So you pay about 43,391 every month. Over 240 months that adds up to about 1.04 crore, which means roughly 54.14 lakh of the total is interest.
Where does each EMI go?
In the first month, interest is the balance times the monthly rate: 5,000,000 x 0.0070833 = 35,417. The rest of the EMI, 43,391 - 35,417 = 7,974, repays principal. The balance falls to 49,92,026, so next month's interest is a little lower and the principal share a little higher. This is why the early years feel like you are barely reducing the loan, and why prepaying early saves so much.
How rate and tenure change the EMI
Keep the loan at 50 lakh and the rate at 8.5%, and change only the tenure.
- 15 years: EMI is about 49,237 and total interest is about 38.63 lakh.
- 20 years: EMI is about 43,391 and total interest is about 54.14 lakh.
- 25 years: EMI is about 40,261 and total interest is about 70.78 lakh.
Going from 20 to 25 years lowers your EMI by about 3,100 a month, but costs you about 16.6 lakh more in interest. Now keep the tenure at 20 years and raise the rate to 9%. The EMI becomes about 44,986, which is about 1,600 a month more, and the total interest rises to about 57.97 lakh.
Common mistakes
- Mixing up the rate. The formula needs the monthly rate, not the yearly one. Using 8.5 instead of 0.0070833 gives an EMI that is far too high.
- Counting years instead of months. n must be in months.
- Forgetting other costs. The formula covers interest and principal only. Processing fees, insurance and stamp duty are separate.
- Expecting the EMI to stay fixed on a floating loan. If the bank changes your rate, the EMI or the tenure changes. Our guide on fixed and floating loans explains how.
Try it yourself
Change the amount, rate and tenure in the calculator and watch the EMI, the interest and the year-by-year breakdown update. The "How this is calculated" section under the calculator shows the same steps with your own numbers.