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Amortization Schedule
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What is EMI?
Definition
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 and principal each month, so that over a specified number of years, the loan is paid off in full."
Details
With most common types of loans, such as real estate mortgages or home loans, the borrower makes fixed periodic payments to the lender over several years with the goal of retiring the loan. EMIs differ from variable payment plans, where the borrower can choose higher payment amounts at their discretion. In EMI plans, borrowers are usually allowed only one fixed payment amount each month.
The benefit of an EMI is that borrowers know precisely how much they need to pay each month, which simplifies personal budgeting.
EMI Formula
The formula for EMI (in arrears) is:
or, equivalently:
Where:
- P = Principal amount borrowed
- A = Periodic amortization payment
- r = Periodic interest rate divided by 100 (annual interest rate also divided by 12 in case of monthly installments)
- n = Total number of payments (for a 30-year loan with monthly payments n = 30 × 12 = 360)
Example Calculation
For example, if you borrow 10,000,000 USD from the bank at 10.5% annual interest for a period of 10 years (i.e., 120 months), then:
EMI can be calculated using the formula:
EMI = P * r * (1 + r)n / ((1 + r)n – 1)
Where:
- P = Principal amount borrowed (10,000,000 USD)
- r = Periodic interest rate (annual interest rate / 12 = 0.00875)
- n = Total number of payments (120 months)
Applying the formula:
EMI = 10,000,000 * 0.00875 * (1 + 0.00875)120 / ((1 + 0.00875)120 – 1) ≈ 134,935 USD
This means you will pay a total of 134,935 USD each month for 120 months to repay the entire loan amount. The total amount payable will be:
134,935 USD * 120 = 16,192,200 USD, which includes 6,192,200 USD as interest.
For more details, you can refer to the Wikipedia - Equated Monthly Installment.