## What is an Equated Monthly Installment (EMI)?

An equated monthly installment (EMI) is a type of payment made by borrowers to lenders on a monthly basis in a fixed amount. EMIs cover both the interest and principal amounts. After a certain number of EMIs being made, the loan will be fully paid off.

**Summary**

**Equated monthly installments (EMIs) are the fixed monthly payments that borrowers make to lenders to pay down their loans.****Each EMI is composed of an interest and a principal repayment, with the payment amount and contribution determined by the total loan principal, tenure, and interest rate.****The reducing-balance EMI calculates interest based on the remaining loan outstanding, which leads to gradually reducing interest payments over time.****The flat-rate EMI calculates interest payments based on the total loan amount, despite the reducing balance outstanding, which leads to a higher total interest payment than the reducing-balance EMI.**

### Understanding Equated Monthly Installments

Borrowers usually make equated monthly installments (EMIs) for many types of loans, such as student loans, auto loans, and home mortgages. EMIs are made on the same day every month at a fixed amount. The borrower will be able to completely pay off the loan at the end of the loan term if EMIs are made as scheduled.

Comparing to variable payment plans, which allow borrowers to make payments at their discretion based on their periodic incomes, EMIs can provide more visibility of the repayment schedule and term to maturity to both borrowers and lenders.

EMIs consist of contributions to both interest and principal, as the portions are unequal and might keep changing. At the end of the loan tenure, the loan will be paid down completely.

### Calculation of EMI

The calculation of EMI requires three inputs: the total principal amount, interest rate, and tenure of the loan. There are two methods to calculate EMI: the flat-rate method and the reduce-balancing method.

#### 1. Flat-Rate Method

In the flat-rate method, each interest payment is calculated based on the total loan amount, regardless of the reducing balance outstanding even though the principal’s been gradually paid down. The EMI amount is calculated by adding the total principal of the loan and the total interest on the principal together, then dividing the sum by the number of EMI payments, which is the number of months during the loan tenure.

For example, a borrower takes a $100,000 loan with a 6% annual interest rate for three years. The total amount of interest during the loan term will be $18,000 (6% * $100,000 * 3), which will be $500 monthly. The EMI amount will be $3,278 [($100,000 + $18,000) / 36]. Thus, the contribution to the principal of each EMI will be $2,778 ($3,278 – $500), which makes up 85% of each EMI, as the interest payment makes up the rest of 15%.

The flat-rate method is particularly used on personal loans and vehicle loans. It is less favorable to borrowers since the interest payments must be made for the entire principal amount, which leads to a higher effective interest rate comparing to the reducing-balance method.

#### 2. Reducing-Balance Method

In contrast to the flat-rate method, the reducing-balance method calculates the interest payment based on the principal outstanding. This means the interest and principal repayment portions of each EMI change overtime. At the early stage of the loan tenure, interest payment makes up a greater portion of the EMI, as a certain percentage of the high principal outstanding.

As the principal is gradually repaid over time, the portion of interest reduces, and greater contributions are made towards principal repayments. The reducing-balance method is usually used on housing mortgages, credit cards, and overdraft facilities.

The reducing-balance EMI can be calculated through the formula below:

Where:

**A**= Periodic EMI amount**P**= Principal borrowed**r**= Periodic interest rate (annual interest rate/12)**n**= Total number of payment (number of months during the loan tenure)

In the reducing-balance method, the EMI payment of the example above will change to $3,040, calculated as below:

The contribution to interest for the first EMI payment is $500 ($100,000 * 0.5%), and the principal repayment is thus $2,542 ($3,042 – $500). For the second month, the interest repayment reduces to $487 [($100,000 – $2,542) * 0.5%], and the principal repayment thus increases to $2,555. The rest of the payments can be calculated with the same method. The repayment schedule is shown in the table below:

As the diagram below shows, the interest payment declines gradually with the loan outstanding, which will be completely paid out and reduced to zero at the 36^{th} month. Here, the total amount of interest payment is $9,519, which is much lower comparing to the $18,000 under the flat-rate method. It makes the reducing-balance method more favorable to borrowers.

### Related Readings

CFI offers the Certified Banking & Credit Analyst (CBCA)™ certification program for those looking to take their careers to the next level. To keep learning and developing your knowledge base, please explore the additional relevant resources below: