Amortisation Schedules: Loan Interest & EMI Explained

An amortisation schedule is a table showing how each instalment of a loan is split between interest and principal repayment, period by period, until the balance reaches zero. Every equal instalment (EMI) pays the interest accrued on the outstanding balance first, and whatever remains reduces the principal.

This matters because the split changes dramatically over the life of a loan: early instalments are mostly interest, later ones mostly principal. Reading a schedule tells you the true cost of borrowing, how much extra payments save, and why the balance falls slowly at first.

Key Concepts

• EMI (equated monthly instalment): the fixed payment that exactly repays the loan with interest over the agreed term.
• Outstanding balance: the amount still owed after each payment. Interest portion: balance × periodic rate. Principal portion: EMI − interest portion.
• Periodic rate (r): the nominal annual rate divided by payments per year. Term (n): the total number of payments.
• Reducing balance: interest is always charged on the current balance, which is why the interest portion shrinks as the loan amortizes.

Formulas

The EMI for principal P, periodic rate r, and n payments is EMI = P × r(1 + r)^n / [(1 + r)^n − 1]. After k payments the outstanding balance is B_k = P(1 + r)^k − EMI × s-angle-k, where s-angle-k = [(1 + r)^k − 1] / r. Each period: interest_k = B_{k−1} × r and principal_k = EMI − interest_k. These assume a fixed rate, equal payments, no prepayments, and no fees.

Worked Example

Borrow ₹6,00,000 at 10% nominal compounded monthly for 10 years. The periodic rate is r = 0.10/12 = 0.00833333 and n = 120. First compute (1.00833333)^120 ≈ 2.70695. Then EMI = 600,000 × 0.00833333 × 2.70695 / (2.70695 − 1) = 600,000 × 0.00833333 × 1.58580870 = ₹7,929.04. Month 1: interest = 600,000 × 0.00833333 = ₹5,000.00; principal = 7,929.04 − 5,000.00 = ₹2,929.04; balance = 600,000 − 2,929.04 = ₹5,97,070.96. Month 2: interest = 597,070.96 × 0.00833333 = ₹4,975.59; principal = 7,929.04 − 4,975.59 = ₹2,953.45; balance = 597,070.96 − 2,953.45 = ₹5,94,117.51. Total paid over 120 months is 7,929.04 × 120 = ₹9,51,484.80, so the total interest is ₹3,51,484.80, more than half the amount borrowed, which shows the cost of a long tenure.

Common Misconceptions

• Banks unfairly front-load interest. No trick is involved: interest each month is simply the rate times the current balance, and the balance is largest at the start, so the interest portion is largest then.
• Extra payments reduce the EMI. The EMI stays fixed; a lump-sum prepayment reduces the outstanding balance, which shortens the remaining tenure and cuts total interest instead.
• A lower EMI is always better. A lower EMI usually means a longer tenure, which raises total interest substantially, as the example's ₹3.51 lakh interest shows.

Real-World Applications

Amortisation schedules structure home loans, car loans, personal loans, and hire-purchase agreements; they let borrowers compare tenures, quantify prepayment savings, and verify that lenders applied the agreed rate correctly.

An amortisation schedule turns a loan into a transparent month-by-month story: each EMI covers that month's interest on the shrinking balance, and the rest chips away the principal until nothing remains.