An equated monthly installment (EMI) is defined by Investopedia as "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 both

interest In finance and economics, interest is payment from a borrower or deposit-taking financial institution to a lender or depositor of an amount above repayment of the principal sum (that is, the amount borrowed), at a particular rate. It is distin ...

and principal each month, so that over a specified number of years, the loan is fully paid off along with interest." It further explains that, with most common types of loans, such as real estate

mortgages A mortgage loan or simply mortgage (), in civil law jurisdicions known also as a hypothec loan, is a loan used either by purchasers of real property to raise funds to buy real estate, or by existing property owners to raise funds for any ...

, 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. The benefit of an EMI for borrowers is that they know precisely how much money they will need to pay toward their loan each month, making the

personal budget A personal budget (for the budget of one person) or household budget (for the budget of one or more person living in the same dwelling) is a plan for the coordination of the resources (income) and expenses of an individual or a household. Purpo ...

ing process easier. The formula for EMI (in arrears) is: :

P \,=\,A\cdot\frac

or, equivalently, :

A \,=\,P\cdot\frac

where: ''P'' is the principal amount borrowed, ''A'' is the periodic

amortization Amortization or amortisation may refer to: * The process by which loan principal decreases over the life of an amortizing loan * Amortization (accounting), the expensing of acquisition cost minus the residual value of intangible assets in a system ...

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 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.

References

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