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Interest and EMI calculator
Three calculators in one: simple interest for class sums, compound interest with yearly, half-yearly, quarterly or monthly compounding, and the EMI of a loan with a year-by-year schedule.
- Made forClass 7 to 12, commerce, families
- Shows the workingEvery step, ready for your practical file
- 3 calculators in oneLoan EMI, Simple interest, Compound interest
Loan EMI
The fixed monthly instalment that repays a loan with interest, and how much of each year goes to interest.
Monthly EMI₹8,791.59for 12 months: you repay ₹1,05,499.06 in all, of which ₹5,499.06 is interest
- EMI
- ₹8,791.59
- Total interest
- ₹5,499.06
- Total repaid
- ₹1,05,499.06
Working
- Monthly rate r = 10 ÷ 12 ÷ 100 = 0.00833333; N = 12 months.
- (1 + r)N = 1.0083333312 = 1.104713.
- EMI = P × r × (1 + r)N ÷ ((1 + r)N − 1) = 1,00,000 × 0.00833333 × 1.104713 ÷ 0.104713 = ₹8,791.59.
- Note: Lenders may round the EMI, add processing fees and insurance, or count interest from the disbursal date, so the loan offer and the statement are the final word. Compare offers using the total amount repaid.
Year by year
| Year | Opening balance | EMIs paid | Principal | Interest | Closing balance |
|---|---|---|---|---|---|
| 1 | ₹1,00,000 | ₹1,05,499 | ₹1,00,000 | ₹5,499 | ₹0 |
| Total | ₹1,05,499 | ₹1,00,000 | ₹5,499 |
Simple interest
Interest only on the amount you started with. The usual sum in class 7 and 8 maths and in many short loans.
Simple interest₹2,400.00Amount after 3 years: ₹12,400.00
- Principal
- ₹10,000.00
- Interest
- ₹2,400.00
- Amount (P + SI)
- ₹12,400.00
Working
- T = 3 years = 3 years.
- SI = P × R × T ÷ 100 = 10,000 × 8 × 3 ÷ 100 = ₹2,400.00.
- Amount = P + SI = 10,000 + 2,400 = ₹12,400.00.
- Tip: For a time in months, divide by 12; for days, divide by 365 (your textbook or bank may say otherwise for a particular question).
Compound interest
Interest is added to the amount at the end of every period and earns interest itself. Choose how often it is added.
Compound interest₹2,597.12Amount after 3 years, compounded yearly: ₹12,597.12
- Amount
- ₹12,597.12
- Compound interest
- ₹2,597.12
- Simple interest would be
- ₹2,400.00compounding earns ₹197.12 more
Working
- A = P × (1 + R ÷ (100 × n))n × T, with n = 1 (yearly).
- A = 10,000 × (1 + 8 ÷ 100)1 × 3 = 10,000 × 1.083 = ₹12,597.12.
- CI = A − P = 12,597.12 − 10,000 = ₹2,597.12.
- Note: Banks may compound on different dates, round at each step or use other rules for part periods, so their figures can differ by a few rupees.
Year by year
| Year | Opening | Interest | Closing |
|---|---|---|---|
| 1 | ₹10,000.00 | ₹800.00 | ₹10,800.00 |
| 2 | ₹10,800.00 | ₹864.00 | ₹11,664.00 |
| 3 | ₹11,664.00 | ₹933.12 | ₹12,597.12 |
What it works out
Understanding interest and EMI
Simple interest is charged only on the amount you started with. Compound interest is added to the amount at the end of every period and then earns interest itself, which is why savings grow faster, and loans cost more, over long periods.
An EMI (equated monthly instalment) is the fixed monthly payment that repays a loan and its interest over the tenure. In the early months most of each EMI is interest; later, most of it repays the loan, as the yearly schedule shows.
Formula and worked example
Working out interest and EMI by hand
The calculator uses exactly these formulas. Write them in your notebook and check one answer by hand: it is the surest way to remember them.
The formula
- SI = P × R × T ÷ 100
- A = P × (1 + R ÷ (100 × n))n × T
- EMI = P × r × (1 + r)N ÷ ((1 + r)N − 1)
- P
- principal: the amount saved or borrowed (₹)
- R
- rate of interest, % a year
- T
- time in years
- n
- times a year interest is added: 1, 2, 4 or 12
- r
- monthly rate = R ÷ 12 ÷ 100
- N
- number of monthly instalments
Worked example
A loan of ₹1,00,000 at 10% a year for 12 months
- Monthly rate r = 10 ÷ 12 ÷ 100 = 0.0083333; N = 12.
- (1 + r)12 = 1.008333312 = 1.104713.
- EMI = 1,00,000 × 0.0083333 × 1.104713 ÷ 0.104713 = ₹8,791.59.
- Total repaid = 8,791.59 × 12 = ₹1,05,499.06, so the interest is ₹5,499.06.
AnswerEMI ₹8,791.59; total interest ₹5,499.06
In projects and exams
How students use it
Simple interest, compound interest by frequency, and a loan EMI with a yearly schedule. Here is where it earns its place in a school year.
Maths chapters on interest
Check simple and compound interest answers, including half-yearly and quarterly compounding.
Commerce and business maths
Work through loan and investment problems with the full working shown.
Comparing loan offers
Compare offers on the total amount repaid, not just the EMI, for an education or vehicle loan.
Seeing savings grow
Watch how compounding and time make a regular saving habit worthwhile.
Check your work
Common mistakes to avoid
These are the slips that cost marks in exams and burn out parts on the bench.
Using the yearly rate as monthly
In the EMI formula r is the monthly rate: 12% a year is 1% a month, written 0.01.
Months in a years formula
In SI = P × R × T ÷ 100, T is in years: 6 months is 0.5.
Forgetting the compounding frequency
Quarterly compounding at 8% a year means 2% per quarter for 4 × T quarters.
Judging a loan by its EMI
A longer tenure lowers the EMI but raises the total interest. Look at the total repaid.
Questions
Questions about interest and EMI
Stuck on a project or a sum? Ask the institute on WhatsApp.
Ask on WhatsAppWhat is the difference between simple and compound interest?
Simple interest is always worked out on the original principal. Compound interest is worked out on the principal plus the interest already added, so it grows faster.
Why does most of an early EMI go to interest?
Interest each month is charged on the balance still owed, which is largest at the start. As the balance falls, the interest part shrinks and more of the same EMI repays the loan.
Is a flat rate the same as a reducing rate?
No. A flat rate charges interest on the full original loan for the whole tenure, so the real cost is higher than the same reducing (balance) rate. This calculator uses the reducing-balance method.
Can I use this for a fixed deposit?
Use the compound interest calculator with the compounding frequency stated in your bank's deposit terms. The bank's own figure is final, since banks can round and compound on particular dates.
Does it include prepayment, fees or insurance?
No. Part-prepayment reduces the interest, and fees and insurance add to the cost; check the lender's terms for each.
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Read more about interest and EMI
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