 # Mathematics of EMI Breakup

## How Breakup of EMI into Interest & Principal is done?

### Introduction

In this article, we are going to discuss the mathematics of EMI breakup in loan repayment, how breakup of EMI into interest and principal is done etc. Many loan borrowers are often confused why major portion of their EMI goes to interest and not principal in the initial period. Let us discuss its reasons in detail here.

### Mathematics of EMI Breakup | How Breakup of EMI into Interest & Principal is done?

#### What is EMI?

• EMI (Equated Monthly Installment) is a loan repayment amount to be paid every month.
• It consists of 2 parts – Principal and Interest. Interest is on the remaining principle amount to be repaid and principal component of EMI is the difference between EMI and interest.
• EMI depends on three factors namely :
1. Amount of loan taken
2. Interest rate on the loan taken and
3. Loan tenure
• With this tool a borrower can actually know pre-hand how much he has to repay each calendar installment. So, this EMI tool forms a part of the budgeting as well as financial planning exercise. Also, since monthly repayment consists of interest and principal both, it allows borrowers to repay the loan in full.
• In the initial period, the total loan amount to be repaid is more.
• In each month, Interest is on the remaining principal amount to be repaid. So, major portion of EMI goes to interest in the initial period.
• With time, interest decreases and principal amount remaining decreases and the loan gets repaid.

#### Calculation of EMI Breakup

##### Case A :
• Let us understand the calculation of EMI breakup with the help of an example.
• Suppose,
• Loan amount (P) is Rs.5,00,000
• Annual interest rate is 12% and
• Tenure of the loan is 2 years.
• Interest rate is given on an annual basis. So, for calculation it has to be converted into periodic basis. Here, the periodicity of paying loan is monthly. Therefore, R = 12% / 12 = 1% = 1 / 100  = 0.01
• No of periods (N) = 12 × 2 = 24 months
• Putting up the values in the above equation, we get EMI = Rs. 23,537
• Now let us see how much principal amount gets repaid in the first month.
• I = 1% of 500,000 = Rs. 5000
• Principal Amount Repaid in first month = EMI – Interest
• Principal Amount Repaid in first month = 23,537 – 5000 = Rs. 18,537
• Loan amount remaining = 5,00,000 – 18,537 = Rs.4,81,463
• So, for second month, I = 1% of 481,463 = Rs. 4,815
• Principal Amount Repaid in the second month = EMI – Interest =  Rs.23,537 – Rs.4,815 = Rs. 18,722
• Loan amount remaining = 4,81,463 – 18,722 = Rs.4,62,741
• Similarly, the interest and principal amount for each month is calculated.

The following table shows the repayment schedule.

##### Case B
• Now suppose the home loan is Rs. 40,00,000
• Interest Rate is 12% and
• Loan tenure is 10 years
• The EMI comes out to be Rs.57,388
##### Comparing EMI Break ups for Case A and Case B :

As can be seen from the above graph, Interest portion is almost 70% of EMI and as we go on repaying the loan, it decreases.

### Conclusion

• It can be concluded from the above 2 graphs that when loan amount and tenure increases, the interest to be paid in the initial period increases.
• This simple EMI calculation helps in knowing the repayment schedule which can be used in decision making while taking a loan.

## 5 thoughts on “Mathematics of EMI Breakup”

1. Samir says:

What changes will be there of someone prepay the emi or preclose the loan

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