An Equivalent Monthly Installment (EMI) is defined by Investopedia as “A fixed amount of payment made by a borrower to a lender on a specified date each calendar month. Equivalent monthly installments are used to repay both interest and principal each months, so that over a certain number of years the loan is fully repaid with interest.”
He further explains that with the most common types of loans, such as home loans , the borrower makes fixed periodic payments to the lender over several years in an effort to repay the loan. EMIs differ from variable payment plans, in which the borrower is able to pay higher payment amounts at their discretion. In EMI plans, borrowers are generally only allowed one fixed payment amount each month.
The advantage of an EMI for borrowers is that they know precisely how much money they will have to pay for their loan each month, which makes the personal budgeting process easier.
The formula for EMI (arrears) is:
or equivalent,
where: P is the principal amount borrowed, A is the periodic amortization payment, r is the annual interest rate divided by 100 (annual interest rate also divided by 12 in case of monthly installments), and n is the total number of payments (for a 30-year loan with monthly payments n = 30 × 12 = 360).
For example, if you borrow 10,000,000 units of a currency from the bank at an annual interest rate of 10.5% for a period of 10 years (i.e. 120 months), then EMI = 10,000,000 currency units × 0.00875 × (1 + 0.00875) 120 /( (1 + 0.00875) 120 – 1) = 134,935 currency units. i.e. you will need to pay a total of 134,935 currency units for 120 months to repay the entire loan amount. The total amount to be paid will be 134,935 × 120 = 16,192,200 currency units, including 6,192,200 currency units as interest on the loan.
