Flat vs Reducing Interest Rate Calculator

About the Flat vs Reducing Interest Rate Calculator

Car, two-wheeler, consumer-durable and many personal and business loans are quoted at a flat rate: interest is charged on the whole amount borrowed for the whole term, even though you repay part of it every month. A home loan, by contrast, is quoted on a reducing balance: interest is charged only on what you still owe. The same number means very different things — a flat 7% over three years costs as much as 12.83% on a reducing balance.

Enter the amount, the rate the lender quoted and the tenure, and this calculator shows both rates, the EMI, the total interest and a month-by-month schedule. Add the processing fee (and the tax on it, where loan fees carry one) to see the APR — the rate including the fee, because the fee comes off the money that reaches you. It converts the other way too: enter a reducing-balance rate to see the flat rate with the same total interest.

Common uses

• Work out what a car or two-wheeler loan quoted at a flat rate really costs.
• Compare a flat-rate dealer offer with a bank loan quoted on a reducing balance.
• Check a consumer-durable or personal loan’s APR against the key fact statement.
• Explain to a buyer or borrower why a lower-looking flat rate is not cheaper.

The two ways interest is charged

Flat rate (also “fixed on the original amount”): total interest = amount × rate × years, and every instalment is (amount + total interest) ÷ number of instalments. Borrow 100,000 at 10% flat for 3 years and the interest is 30,000 whatever you repay in the meantime; the EMI is 3,611.11.

Reducing balance: each month’s interest is the balance × the yearly rate ÷ 12, and the EMI is amount × i ÷ (1 − (1 + i)^−n). As the balance falls, so does the interest, and more of each EMI goes to the principal.

The two meet only for a single-instalment loan. Over a longer term the average balance is roughly half the amount borrowed, so a flat rate is worth close to twice as much: the equivalent reducing rate is a little under 2n ÷ (n + 1) × the flat rate, where n is the number of instalments — and well under it for a high rate or a long term (10% flat over five years is 17.27%, not 19.7%). The calculator finds the exact rate instead of estimating it.

How the equivalent rate is found

The flat loan’s instalments are a fact: 3,611.11 a month for 36 months against 100,000 received. The equivalent reducing-balance rate is the rate at which those instalments exactly repay the loan — its internal rate of return, found here by bisection and stated as a yearly rate (monthly rate × 12), the way an APR is computed under US Regulation Z, appendix J: “the unit-period rate × the number of unit-periods in a year”. The effective annual rate, (1 + monthly rate)^12 − 1, is a little higher (19.46% for this loan); the APR ↔ APY converter explains the difference.

The other direction is arithmetic: work out the EMI at the reducing rate, add up the instalments, subtract the amount borrowed, and divide the interest by the amount and the years.

Fees, and the rate in your loan papers

A processing or documentation fee is usually deducted before the money reaches you, so it raises the true rate without changing the EMI. The calculator puts the fee (with the tax you enter on it) into the APR by discounting the instalments against what you actually receive.

In India the Reserve Bank requires lenders to give a key fact statement for retail and MSME term loans, with an APR — the “annual cost of credit to the borrower which includes interest rate and all other charges associated with the credit facility” — and charges collected for third parties, such as insurance and legal fees, are part of it (RBI circular on the Key Facts Statement). If your sanction letter quotes a flat rate, ask for the key fact statement and compare its APR with the figure here. For several offers side by side, use the loan comparison calculator.

Limitations

• Interest is worked out monthly (rate ÷ 12), as lenders calculate EMIs. A lender that charges daily interest or rounds the EMI can differ by small amounts.
• The schedule of a flat-rate loan is shown on a reducing basis, which is how lenders state the amount left to repay; your lender’s foreclosure statement may use its own method, so check the agreement before you prepay.
• Insurance added to the loan, late-payment charges, part-payment limits and tax benefits are not included.
• Prepayment is not modelled here. A flat-rate loan usually saves little or nothing when you prepay, because the interest was fixed at the start.

Privacy

Everything is calculated in your browser. The amounts and rates you enter are never uploaded or stored.