What is an EMI?
An equated monthly instalment (EMI) is the fixed amount a borrower pays every month to repay a loan with interest over a set period. Each EMI has two parts: interest on the outstanding balance and repayment of principal.
Reducing-balance method
Interest is charged only on the amount still owed. If P is the loan, i the monthly interest rate and n the number of monthly instalments, then EMI = P·i·(1 + i)ⁿ / [(1 + i)ⁿ − 1]. This comes from treating the EMIs as an ordinary annuity whose present value equals the loan.
- For an annual rate of 12%, i = 0.12/12 = 0.01.
- Example: P = ₹1,00,000, 12% p.a., 12 months: EMI = 100000 × 0.01 × 1.01¹²/(1.01¹² − 1) ≈ ₹8,884.88. Total paid ≈ ₹1,06,618.55, so total interest ≈ ₹6,618.55.
- Example: P = ₹20,000 at 1% per month repaid in 2 instalments: EMI = 20000 × 0.01 × 1.0201/0.0201 ≈ ₹10,150.25.
As instalments are paid, the outstanding balance falls, so the interest part of each EMI decreases and the principal part increases, though the EMI itself stays the same.
Flat-rate method
Interest is calculated on the original principal for the whole period: EMI = (P + P × r × t)/(number of months), where r is the annual rate and t is in years. Example: ₹60,000 at 10% p.a. flat for 2 years: interest = 12,000, total = 72,000, EMI = 72,000/24 = ₹3,000. The flat-rate method costs the borrower more than a reducing-balance loan at the same quoted rate, because interest is charged even on principal already repaid.
Key points
- Use the monthly rate i and the number of months n in the EMI formula.
- Reducing balance: interest part falls, principal part rises over time.
- Total interest = n × EMI − P.
- Flat rate: interest on the original principal throughout.
Exam tips
- Check the answer roughly: the EMI must be a little more than P/n.
- Read whether the rate is "flat" or on "reducing balance".