Simple and compound interest calculator

The two formulas, in one place

Simple interest SI equals P times r times t, divided by 100. Compound interest CI equals P times (1 plus r divided by 100 divided by n) raised to the power of (n times t), minus P. In both: P is the principal, r is the annual rate in per cent, t is the time in years, and n is the number of compounding periods a year. For annual compounding, n is 1 and the CI formula collapses to P times (1 plus r divided by 100) raised to the power of t, minus P.

Simple interest grows by a fixed rupee amount each year. Compound interest grows each year on the previous year's balance, so its rupee growth accelerates. This is the single idea that turns a saving habit into a corpus and a carried-over card balance into a large sum.

Worked example a student can reproduce

P equals ₹1,00,000, r equals 8 per cent, t equals 10 years, annual compounding (n equals 1). SI equals 1,00,000 times 8 times 10, divided by 100, which is ₹80,000. For CI, compute (1.08) to the tenth power first: that is about 2.1589. Subtract 1 and multiply by the principal: 1,00,000 times 1.1589 equals ₹1,15,892 of compound interest. The gap, ₹35,892, is the compounding effect over the decade.

The gap grows roughly with the square of the years in the early phase, and faster after that.

The two-year shortcut every bank-exam student should know

For exactly two years of annual compounding, there is a tidy closed form. CI minus SI equals P times (r divided by 100) squared. No powers, no logarithms, just a squared fraction. At ₹1,00,000 and 10 per cent for two years: the gap is 1,00,000 times (0.1) squared, which is ₹1,000. Check with the full formulas: SI equals ₹20,000; CI equals 1,00,000 times 1.21 minus 1, which is ₹21,000. The gap is ₹1,000.

This shortcut only works for two years and only for annual compounding. It is useful in bank, SSC and school exams, where interest sums are often set at a two-year horizon with yearly compounding because it keeps the arithmetic reproducible. The page prints the shortcut's value alongside the full calculation so the two can be checked against each other.

Rule of 72 and its honest accuracy

Years to double a sum at a fixed compound rate is close to 72 divided by that rate in per cent. At 6 per cent, it says 12 years. At 8 per cent, 9 years. At 12 per cent, 6 years. The actual figure uses the natural logarithm of 2, divided by the natural logarithm of (1 plus the rate as a decimal).

The rule is most accurate near 8 per cent. It is a good mental shortcut inside the 5 to 10 per cent band that covers most Indian savings products. Outside that band, use the exact formula; the error is small on either side but visible past 15 per cent.

Finding the rate when the target and the term are set

Set the mode to 'Find the rate'. Enter P, the target and the years. The formula for the required rate is: r equals ((target divided by P) to the power of (1 divided by (n times t)), minus 1), multiplied by n times 100. For annual compounding (n equals 1), this collapses to ((target divided by P) raised to (1 divided by t), minus 1) multiplied by 100.

Example: double ₹1,00,000 in ten years, annual compounding. The required rate is (2 raised to the 0.1 power minus 1) times 100, which equals about 7.18 per cent. That is a cleaner answer than the Rule of 72 suggests; the rule is a mental shortcut, not a precise solver.

Finding the time when the rate is set

Set the mode to 'Find the time'. The formula is: t equals natural-log of (target divided by P), divided by the product of n and natural-log of (1 plus r divided by (100 times n)). For annual compounding, it simplifies to log(target divided by P) divided by log(1 plus r divided by 100).

Example: at 7 per cent compounded annually, how long until ₹1,00,000 becomes ₹2,00,000? ln(2) is 0.6931. ln(1.07) is 0.0677. The ratio is 10.24 years. Rule of 72 would say 10.29 years; close but not identical, and the page prints both so the shortcut can be sized against the real answer.

How each input moves the answer

The rate matters most. In compare mode at ten years and annual compounding, lifting the rate from 6 to 8 per cent raises compound interest from about ₹79,085 to ₹1,15,892. Simple interest rises in a straight line from ₹60,000 to ₹80,000, so the gap widens quickly.

The compounding frequency works at the margin. Moving from annual to monthly compounding at the same 8 per cent for ten years lifts the compound interest from about ₹1,15,892 to about ₹1,21,964. Simple interest is unchanged at ₹80,000 either way; simple interest does not have a compounding frequency.

The term works the hardest over long horizons. A ten-year term versus a thirty-year term, at the same 8 per cent annual, gives compound interest of about ₹1,15,892 against ₹9,06,266. That is nearly eight times more for three times the years.

Where simple and compound interest actually appear

Flat-rate loans (sometimes seen in dealer finance on two-wheelers) compute interest as simple interest on the original principal for the full tenure, which is why the stated rate understates the real cost. Fixed deposits, recurring deposits, PPF, EPF and bonds all compound; the frequency differs, but the formula is one of those above. Mutual fund returns are reported as CAGR, which is the compound rate that would turn the starting value into the ending value over the term.

Credit card finance compounds on a monthly basis at a rate that is often 3 to 4 per cent a month. Over a year that is 42 to 60 per cent effective, which is why a carried-over card balance grows so quickly. Home loans, car loans, personal loans, education loans and bike loans run on reducing-balance EMI, which is compound-interest arithmetic wearing a different name.

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