The EMI Formula: How to Compute It and Why It Works

The EMI Formula

An equated monthly installment (EMI) is the fixed amount you pay each month to repay a loan. The standard formula used for most loans is:

EMI = P × r × (1+r)^n / ((1+r)^n - 1)

where P is the principal loan amount, r is the monthly interest rate, and n is the number of monthly payments.

Sources: marketfeed, CRED, Bajaj Finance, Omni Calculator, SoFi, Corporate Finance Institute, Butter Money

each variable: P, r, n

Each variable in the formula has a specific meaning:

P (Principal) is the amount you borrow. It is the original loan amount before any interest is added.

r (Monthly interest rate) is the annual interest rate divided by 12, expressed as a decimal. For example, an annual rate of 10% becomes 0.10 / 12 = 0.00833 per month.

n (Number of monthly payments) is the loan tenure expressed in months. For a 5-year loan, n = 5 × 12 = 60 months.

• P: the loan principal, in the same currency as the EMI.
• r: monthly interest rate, calculated as annual rate / 12, in decimal form.
• n: total number of monthly installments (years × 12).

Sources: marketfeed, CRED, Omni Calculator, SoFi, Butter Money

Derivation of the Formula

The formula comes from the reducing-balance method, where interest is calculated on the outstanding principal each month. As you pay, the outstanding balance decreases, so the interest portion of each payment also decreases while the principal portion increases.

The derivation starts with the future value of a series of equal payments. For a loan, the present value of all future EMIs must equal the principal. Solving that equation for the payment amount yields the formula above.

Sources: marketfeed, Bajaj Finance, SoFi, Corporate Finance Institute

Worked Example with Numbers

Let's calculate the EMI for a loan of ₹1,00,000 at an annual interest rate of 10% for 12 months. First, convert the annual rate to a monthly rate: r = 10% / 12 = 0.833% per month, or 0.00833 in decimal. Here, n = 12 months.

Plugging these into the formula: EMI = 100000 × 0.00833 × (1.00833)^12 / ((1.00833)^12 - 1). The result is approximately ₹8,792 per month. This matches the example provided by marketfeed and CRED.

Sources: marketfeed, CRED

Using the formula in Excel

In spreadsheet software, you can use the built-in PMT function instead of entering the formula manually. The syntax is =PMT(rate, nper, pv), where rate is the monthly interest rate, nper is the number of months, and pv is the loan principal entered as a negative value.

For example, for a ₹10,00,000 loan at 10% annual interest for 5 years (60 months), you would enter =PMT(0.10/12, 60, -1000000), which returns approximately ₹21,247.

• In Excel: =PMT(rate, nper, pv)
• rate: monthly interest rate (annual rate / 12)
• nper: total number of months
• pv: loan amount as a negative number

Sources: Butter Money, marketfeed

Common Errors to Avoid

A frequent mistake when manually calculating EMI is using the annual interest rate instead of converting it to a monthly rate. Always divide the annual rate by 12 and convert to a decimal.

Another error is mixing up the number of periods. Use months, not years, for n. For a 5-year loan, n is 60, not 5.

Sources: Butter Money