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EMI Calculator: Reducing Balance vs Flat Rate
Enter the loan amount, rate and tenure to get the equated monthly instalment. The tool also shows what the same percentage costs on the other basis, and the true rate hidden inside a flat quote.
What an EMI is and how it is calculated
An equated monthly instalment (EMI) is a fixed payment made every month until the loan is repaid. On a reducing-balance loan, which is the normal basis for home, car and many personal loans, interest each month is charged on what you still owe. The EMI follows the formula:
EMI = P × r × (1 + r)n ÷ ((1 + r)n − 1)
where P is the principal, r is the monthly rate (annual rate ÷ 12 ÷ 100) and n is the number of months. Early instalments are mostly interest, later ones mostly principal.
How a flat rate works
With a flat rate, interest is computed once on the original amount for the entire tenure: Interest = P × rate × years. The total is then divided into equal monthly parts: EMI = (P + Interest) ÷ n. Because you repay principal every month but are still charged as if you owed all of it, the effective cost is much higher than the quoted rate suggests.
To compare fairly, the tool finds the reducing-balance rate that produces the same EMI, using bisection on the payment formula. That figure is the one to set beside a bank's reducing-balance quote. As a rough guide, the equivalent rate is often close to, but a little under, twice the flat rate for longer tenures.
Reading the comparison
- Total interest: total of all instalments minus the amount borrowed.
- Equivalent rate: lets you compare a flat offer against a reducing-balance offer on equal terms.
- Interest difference: how much more or less the other basis would cost at the same quoted percentage.
Processing fees, insurance and prepayment charges are excluded. If an offer includes them, use the APR calculator to find the all-in rate.
Practical points
Ask any lender whether the rate is flat or reducing before you compare numbers. Check how part-prepayments are treated, because on a flat-rate loan prepaying often saves much less than it would on a reducing-balance loan. Keep each EMI within a share of income you can sustain, and for a single loan with a yearly breakdown try the loan calculator.
Checking a lender quote
When a lender quotes a monthly instalment, multiply it by the number of months and divide the total by the amount borrowed. Compare the implied reducing-balance rate with the rate in the offer. A large gap usually means a flat rate, processing fees or insurance is built in. Ask for the annual percentage rate or total cost of credit in writing before you sign.
Worked example
A lender offers 300,000 at a 9% flat rate over three years. What is the EMI and what reducing-balance rate does it really equal?
Inputs
| Loan amount | 300000 |
|---|---|
| Quoted annual interest rate | 9 % |
| The quoted rate is | Flat rate |
| Tenure | 3 |
| Tenure is in | Years |
Result
Flat rate EMI for 36 months.
| Total payable | 381,000.00 |
|---|---|
| Total interest | 81,000.00 |
| Equivalent reducing-balance rate | 16.24% a year |
| EMI if 9.00% were charged on the reducing balance | 9,539.92 |
| Interest difference between the two bases | 37,562.89 |
- A flat rate is charged on the full original amount for the whole tenure, so its true cost is well above the quoted number.
Financial disclaimer: Results are estimates for planning and education. They are not financial, tax or legal advice. Fees, taxes, rates and rules vary by lender, product and country, so confirm figures with your provider or a qualified adviser before making decisions.
Frequently asked questions
How is EMI calculated?
On a reducing-balance loan, EMI equals the principal times the monthly rate times the growth factor raised to the number of months, divided by that growth factor minus one. This page calculates it for you.
What is the difference between flat and reducing-balance interest?
Flat interest is charged on the original loan amount for the whole tenure. Reducing-balance interest is charged only on the outstanding balance, which falls with every instalment.
Is a flat rate of 8% the same as 8% reducing?
No. At the same percentage, the flat-rate loan costs far more because you keep paying interest on money you have already repaid. The equivalent reducing rate is noticeably higher than 8%.
Does a lower EMI mean a cheaper loan?
Not necessarily. A longer tenure lowers each instalment but raises total interest. Compare the total interest as well as the EMI.
Can I use this EMI calculator for any currency?
Yes. The maths does not depend on the currency, so enter the amounts in whichever one you use.
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References and sources
- Standard annuity formula and the flat-to-effective rate relationship as taught in introductory finance courses.
- Consumer Financial Protection Bureau: educational material on loan costs and APR. Link