Percentage & EMI Calculator

about this tool

Six percentage questions

Every percentage problem is one of a handful of questions, so the tool asks which one rather than offering a bare formula. What is 15% of 80 (12). 12 is what percent of 80 (15%). Percent change from 80 to 100 (a 25% increase; from 100 to 80 is a 20% decrease, because the base changed). 50 with 20% off (40, saving 10). 1250 plus 18% (1475, for tax, tip or markup). And the one people get wrong: 120 is 20% more than what? The answer is 100, found by dividing by 1.2, not 96, which is what subtracting 20% of the final price gives. Each answer comes with its working on one line, and floating-point noise is cleaned before display, so 10% of 0.3 is 0.03 rather than 0.030000000000000002.

When both figures in a percent change are 100 or under, the tool also states the difference in percentage points, since a rate going from 10% to 15% has risen five points and fifty percent at once, and headlines routinely confuse the two.

The loan

The EMI is the standard formula for a level payment on a reducing balance with the nominal annual rate compounded monthly — the one banks, spreadsheets (PMT) and every other calculator use, so the figures match. The schedule rounds the way a statement does: the payment to two decimals, each month's interest to two decimals, and the final instalment set to whatever clears the balance, so the principal column sums to the amount borrowed exactly and the loan never ends a cent short or a cent over. Interest at 0% is handled as a straight division rather than a formula that divides by zero.

An extra amount each month is applied to the balance immediately. The tool reruns the schedule and reports the months saved and the interest never charged; the last payment is only what is left, not a full EMI plus the extra.

Flat rates

Some lenders quote a flat rate: interest on the original amount for the whole term, regardless of how much has been repaid. It sounds cheaper than it is. The flat-rate mode builds that schedule — a constant interest charge every month — and then solves, by bisection on the EMI formula, for the reducing-balance rate that would cost exactly the same. Ten percent flat over three years comes out near 17.9% reducing; that is the number to compare with other offers.

Working backwards

How much can I borrow inverts the formula: the payment you can afford, the rate and the term give the principal, and the schedule for that loan follows. The same inversion, solved for the rate, is what the flat-rate comparison uses.

Limits

Payments are monthly; fortnightly or weekly schedules, daily-accrual mortgages and rates that change mid-term are not modelled. Fees, insurance and processing charges are not included, so the figure shown is the interest cost, not the APR. Terms are capped at 600 months and rates at 100% a year. Amounts are unitless — type them in whatever currency you borrow in — and grouped with commas for display.

For free-form arithmetic rather than a fixed form, the math expression evaluator takes a whole expression at once. Amounts in another currency or unit go through the unit converter first.

questions

How is EMI calculated?

EMI = P × i × (1 + i)ⁿ ÷ ((1 + i)ⁿ − 1), where P is the amount borrowed, i the monthly rate (the annual rate divided by 12 and by 100) and n the number of months. Each payment first covers that month’s interest on the balance still owed and the rest reduces the balance, so early payments are mostly interest and late ones mostly principal.

What is the difference between a flat rate and a reducing-balance rate?

A reducing-balance rate charges interest only on what you still owe; a flat rate charges it on the original amount for the whole term, even after most of it is repaid. A 10% flat rate over three years costs the same as roughly 17.9% on a reducing balance, so flat rates are only comparable after converting them.

How do I work out a price before tax or a discount?

Divide, do not subtract. A price of 120 that includes 20% tax was 120 ÷ 1.2 = 100 before it; taking 20% off 120 gives 96, which is wrong because the 20% was charged on the smaller original figure. The tool’s “before %” question does this and shows both figures.

What is the difference between percent and percentage points?

A rate moving from 10% to 15% has risen five percentage points, but by 50 percent, because 5 is half of 10. Newspapers mix the two up constantly; the tool shows both when the figures look like percentages.

How much interest does an extra monthly payment save?

Every extra unit reduces the balance immediately, so it stops earning interest for the rest of the term. Type an amount in “extra each month” and the tool reruns the schedule, reports how many months earlier the loan ends and the interest that is never charged, which on a long mortgage is often a substantial share of the amount borrowed.