Banking and Insurance - Laws and Practice · Calculation of Interest and Annuities

Loan Amortisation and EMI Calculation Explained

Updated 11 October 2026 · Fact-checked

An EMI is the fixed monthly payment that repays a loan with interest. It is the instalment whose present value, at the monthly interest rate, equals the loan amount. Use EMI = P × r × (1+r)^n ÷ [(1+r)^n − 1]. Each month, interest is the opening balance × r. The rest of the EMI repays principal.

Understand Loan Amortisation and EMI Calculation

A loan repaid in equal monthly instalments is an annuity. The bank lends you a sum today. You pay back a fixed amount every month. The loan amount is the present value of all those future payments, discounted at the monthly interest rate. This is why EMI problems are annuity problems.

The interest is charged on the reducing balance. Each month the bank charges interest only on the principal still unpaid. In month 1 the balance is the full loan, so interest is high and principal repayment is small. As the balance falls, interest falls. Since the EMI is fixed, the principal part rises every month.

A table that shows this month by month is an amortisation schedule. Its columns are: opening balance, EMI, interest, principal repaid, closing balance. The closing balance after the last EMI must be nil. Use this as your check.

Under the flat rate method, interest is worked out on the original loan for the whole term, as if nothing were repaid. Interest = P × rate × years. Add it to the loan and divide by the number of months. Because you repay principal every month but still pay interest on the full amount, the true cost is higher than the quoted rate. A flat rate of 10% costs far more than a reducing-balance rate of 10%.

Key rules to remember

Monthly rate: r = annual rate ÷ 12 ÷ 100; Convert the annual rate to a monthly decimal. 12% p.a. gives r = 0.01. n is the number of months, so 3 years gives n = 36.
EMI (reducing balance): EMI = P × r × (1+r)^n ÷ [(1+r)^n − 1]; P is the loan amount. This is the annuity formula rearranged to find the payment.
Loan as present value of EMIs: P = EMI × [1 − (1+r)^(−n)] ÷ r; Use it to find the loan amount from a given EMI, or to check an answer.
Interest for a month: Interest = opening balance × r; Always charged on the balance at the start of the month.
Principal and closing balance: Principal repaid = EMI − interest; closing balance = opening balance − principal repaid; The closing balance of one month is the opening balance of the next.
Total interest: Total interest = (EMI × n) − P; Holds when all n EMIs are paid as scheduled. The last EMI may differ slightly because of rounding.
Flat rate EMI: EMI = [P + (P × annual rate × years)] ÷ (years × 12); Interest is on the original principal for the whole term. No reduction for repayments.

How to solve Loan Amortisation and EMI Calculation questions

Follow the same order for every EMI or amortisation question. It keeps the working clear and easy for the examiner to mark.

1Read the question and note P, the annual rate, the term and whether interest is on reducing balance or flat.
2Convert to monthly terms: r = annual rate ÷ 12 ÷ 100 and n = years × 12.
3If the rate is flat, compute total interest = P × rate × years, add it to P and divide by n. Stop there.
4If the rate is reducing balance, compute (1+r)^n first, then apply EMI = P × r × (1+r)^n ÷ [(1+r)^n − 1].
5For a schedule, take each month in turn: interest = opening balance × r, principal = EMI − interest, closing = opening − principal.
6Check the work: the principal parts should add up to P, and the last closing balance should be nil or a small rounding difference.
7State the answer in rupees with units, and add one line of comment, for example total interest paid or the effect of the method.

Quickest way: Compute EMI once, then roll the balance

When to use it: Use it when the question asks for the EMI plus the split in the first one or two months, or the balance after a few instalments.

Find (1+r)^n once and keep at least five or six decimal places. Rounding here spoils the EMI.
Compute the EMI, then round it to the nearest paisa or rupee as the question states.
Do only the months asked. For month 1, interest = P × r and principal = EMI − interest.
For the next month, use the closing balance as the new opening balance and repeat.
If the question gives the (1+r)^n value or an annuity factor, use it directly instead of recomputing.

Common mistakes in Loan Amortisation and EMI Calculation

Using the annual rate with the number of months in the formula.
The loan is described in years and the rate in per cent per annum, so the units get mixed.
Fix: Convert both to months first: r = annual rate ÷ 12 ÷ 100 and n = years × 12.
Charging interest on the original loan every month in a reducing-balance schedule.
Students carry over the flat-rate idea.
Fix: Interest each month = opening balance × r. Opening balance falls every month by the principal repaid.
Treating the EMI as split equally between principal and interest, or taking a fixed principal each month.
Equal total payment is confused with equal principal.
Fix: The EMI is fixed but the split changes. Interest falls and principal rises every month.
Rounding (1+r)^n early, for example to 1.13 instead of 1.126825.
Wanting to save time on the calculation.
Fix: Keep at least five decimal places until the final EMI. Round only at the end.
Saying a flat rate and a reducing-balance rate with the same number cost the same.
The rates look identical on paper.
Fix: Under flat rate, interest is on the full original loan throughout, so the effective cost is higher. Compare the EMI or total interest to show it.
Forgetting to deduct principal repaid from the balance, or deducting the whole EMI.
Rushing through the schedule.
Fix: Closing balance = opening balance − (EMI − interest). Only the principal part reduces the loan.

Worked examples

Example 1

A bank sanctions a term loan of ₹10,00,000 at 12% p.a. on reducing balance, repayable in 12 equal monthly instalments. Calculate the EMI and show the interest and principal split for the first two months.

Show the solution

P = ₹10,00,000. r = 12 ÷ 12 ÷ 100 = 0.01. n = 12.
(1.01)^12 = 1.126825 (approx.).
EMI = 10,00,000 × 0.01 × 1.126825 ÷ (1.126825 − 1) = 11,268.25 ÷ 0.126825 = ₹88,848.79 (approx.).
Month 1: opening balance ₹10,00,000. Interest = 10,00,000 × 0.01 = ₹10,000. Principal = 88,848.79 − 10,000 = ₹78,848.79. Closing balance = ₹9,21,151.21.
Month 2: opening balance ₹9,21,151.21. Interest = ₹9,211.51. Principal = 88,848.79 − 9,211.51 = ₹79,637.28. Closing balance = 9,21,151.21 − 79,637.28 = ₹8,41,513.93.
Observation: interest has fallen from ₹10,000 to ₹9,211.51 and principal has risen, while the EMI stays fixed.

Answer: EMI ≈ ₹88,848.79. Month 1: interest ₹10,000 and principal ₹78,848.79. Month 2: interest ₹9,211.51 and principal ₹79,637.28.

Example 2

A vehicle loan of ₹5,00,000 is offered at 10% p.a. flat for 3 years, repayable in 36 equal monthly instalments. Calculate the EMI. Compare it with the EMI on a 10% p.a. reducing-balance loan for the same amount and term, and comment.

Show the solution

Flat method: interest = 5,00,000 × 10% × 3 = ₹1,50,000.
Total repayable = 5,00,000 + 1,50,000 = ₹6,50,000.
Flat EMI = 6,50,000 ÷ 36 = ₹18,055.56.
Reducing method: r = 10 ÷ 12 ÷ 100 = 0.0083333. n = 36. (1+r)^36 = 1.348182 (approx.).
EMI = 5,00,000 × 0.0083333 × 1.348182 ÷ 0.348182 = 4,166.67 × 3.87208 = ₹16,133.6 (approx.).
Total interest on reducing balance = 16,133.6 × 36 − 5,00,000 = 5,80,810 − 5,00,000 = about ₹80,800.
Difference in EMI = 18,055.56 − 16,133.6 = about ₹1,922 a month.

Answer: Flat EMI = ₹18,055.56 with total interest ₹1,50,000. Reducing-balance EMI ≈ ₹16,134 with total interest of about ₹80,800. The same quoted 10% costs far more under the flat method, because interest is charged on the full ₹5,00,000 even as the loan is repaid.

Exam tips

Show r and n explicitly at the start. Examiners give marks for correct conversion even if the arithmetic slips later.
Write the formula before substituting. In a written paper, method marks depend on it.
If the question asks for a schedule, present it as a neat table-like list with the five columns, and check that the final balance is nil or only a rounding difference.
In flat versus reducing questions, give both EMIs and one line of comment on effective cost. The comment often carries marks.
Keep intermediate values to five or six decimals and state that you have rounded the final answer to the nearest rupee or paisa.

Practice questions from Calculation of Interest and Annuities

Loan Amortisation and EMI Calculation in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

NISM CertificationsLoan Pricing, Interest Rates and EMI Calculation

Loan Amortisation and EMI Calculation: frequently asked questions

How do I calculate EMI with a formula?

Use EMI = P × r × (1+r)^n ÷ [(1+r)^n − 1]. Here P is the loan, r the monthly rate as a decimal and n the number of months. For ₹10,00,000 at 12% p.a. for 12 months, the EMI is about ₹88,849.

What is the difference between flat rate and reducing balance interest?

Under the flat rate method, interest is on the original loan for the whole term. Under reducing balance, interest each month is on the unpaid balance only. For the same quoted rate, the flat method costs more.

How does an EMI split into principal and interest?

Interest for the month is the opening balance × the monthly rate. The principal part is the EMI minus that interest. Early EMIs have more interest and later EMIs have more principal.

Can I check my EMI answer quickly?

Yes. Complete the schedule and see whether the closing balance after the last instalment is nil, apart from rounding. You can also check that EMI × [1 − (1+r)^(−n)] ÷ r gives back the loan amount.