Equated monthly installment

Anequated monthly installment (EMI)is a fixed payment amount made by a borrower to a lender at a specified date each calendar month. Equated monthly installments are used to pay off bothinterestandprincipaleach month, so that over a specified number of years, theloanis fully paid off along with interest.

As with most common types of loans, such as real estatemortgages,the borrower makes fixed periodic payments to the lender over the course of several years with the goal of retiring the loan. EMIs differ from variable payment plans, in which the borrower is able to pay higher payment amounts at his or her discretion. In EMI plans, borrowers are mostly only allowed one fixed payment amount each month.

Formula

The formula for EMI (in arrears) is:

$P\,=\,A\cdot {\frac {1-\left({1+r}\right)^{-n}}{r}}$

or, equivalently,

$A\,=\,P\cdot {\frac {r(1+r)^{n}}{(1+r)^{n}-1}}$

Where:Pis the principal amount borrowed,Ais the periodicamortizationpayment,ris the annual interest rate divided by 100 (annual interest rate also divided by 12 in case of monthly installments), andnis the total number of payments (for a 30-year loan with monthly paymentsn= 30 × 12 = 360).

For example, if you borrow 10,000,000 units of a currency from the bank at 10.5% annual interest for a period of 10 years (i.e., 120 months), then EMI = units of currency 10,000,000 × 0.00875 × (1 + 0.00875)¹²⁰/((1 + 0.00875)¹²⁰– 1) = units of currency 134,935. i.e., you will have to pay total currency units 134,935 for 120 months to repay the entire loan amount. The total amount payable will be 134,935 × 120 = 16,192,200 currency units that includes currency units 6,192,200 as interest toward the loan.