Compound Interest Calculator

Compound interest is interest calculated on your original amount and on the interest that has already been added to it. Simple interest pays only on what you started with. Compound interest pays on the balance — and the balance grows every time interest is credited.

The consequence is that the amount earned in each period rises even though the rate never changes. Nothing is accelerating except the base the calculation runs on. That is the entire mechanism, and it is why the difference between compound and simple interest is barely visible over a year and impossible to miss over twenty.

One clarification worth making early, because this page is full of rupee figures: a compound interest calculation is arithmetic, not a product and not a forecast. It answers exactly one question — if this amount grows at this rate, compounded this often, for this long, what is it worth at the end? Whether anything actually grows at that rate is a separate question the arithmetic cannot answer.

Five things decide every figure this calculator produces:

• Principal — the amount you start with. Everything scales directly from it.
• Interest rate — an assumed nominal annual rate. This is the input the answer is most sensitive to and the one nobody can know in advance.
• Compounding frequency — how often interest is added to the balance, which changes what a given nominal rate actually delivers.
• Time— the input the result bends most sharply with, because each period’s interest becomes part of the base for the next.
• Reinvestment of interest — the assumption underneath all of it. Compounding only happens if interest stays in. Interest that is withdrawn as it is earned is simple interest by another name.

A worked example makes the mechanism visible. ₹1,00,000 at 10% compounded annually:

1Year 1    balance ₹1,00,000   interest ₹10,000    ends ₹1,10,0002Year 2    balance ₹1,10,000   interest ₹11,000    ends ₹1,21,0003Year 3    balance ₹1,21,000   interest ₹12,100    ends ₹1,33,1004...5Year 10   balance ₹2,35,795   interest ₹23,579    ends ₹2,59,3746 7Same 10% every year. The interest earned in year 108is more than double the interest earned in year 1.

Year one earns ₹10,000 and year ten earns ₹23,579, at an identical rate. Nothing changed except the balance the rate was applied to.

The formula this calculator uses, for periodic compounding:

1A = P(1 + r/n)^(nt)2 3A  =  the future value, principal and interest together4P  =  the principal — what you start with5r  =  the annual interest rate as a decimal (10% is 0.1)6n  =  compounding periods per year (annual 1, monthly 12)7t  =  time in years8 9Compound interest:  CI = A - P

Two variables cause almost all the confusion. r is a decimal, not a percentage — writing 10 instead of 0.1 inflates the answer beyond recognition. And n appears twice, dividing the rate and multiplying the exponent: more periods each earn a smaller share, but there are more of them, and the second effect slightly outweighs the first.

When the rate is zero the formula gives A = P × 1^(nt) = P, so the future value is the principal and the interest is nothing. This calculator handles that case explicitly rather than relying on the arithmetic, so the figures come out exact and the schedule adds up cleanly.

Where regular contributions are involved, the future value is the principal grown by the formula above, plus the contribution stream grown by the annuity formula FV = PMT × [((1+i)^N − 1) / i]. The calculator builds the schedule directly rather than applying either formula once, and the two agree — that agreement is asserted across several thousand combinations in the test suite.

1. Enter the principal. The amount you are starting with.
2. Enter the annual interest rate. As a percentage — the calculator converts it. This is an assumption you are choosing, not a rate being offered.
3. Select the compounding frequency. Annually, semi-annually, quarterly, monthly or daily.
4. Enter the duration. In years and months.
5. Read the estimated future value. It updates as you type.
6. Subtract the principal to get the compound interest. The calculator shows both, so there is nothing to work out by hand.

If you want to add money along the way, switch contributions on and choose monthly or yearly. The schedule is built from your actual contribution dates rather than approximated, and the timing convention it uses is stated on screen.

Simple interest is SI = P × r × t. It pays on the principal alone, every period, forever. Compound interest pays on the balance, which includes interest already credited. On ₹1,00,000 at 10% over 10 years with annual compounding:

The same rate, the same principal and the same duration produce a difference of ₹59,374. Compounding accounts for interest being added to the balance and subsequently earning interest of its own, according to whichever compounding convention applies.

Over a single year with annual compounding the two are identical — interest is credited once, at the end, with nothing left to compound on. Everything after that first year is the gap widening. To run the other side of that comparison on your own figures, the simple interest calculator applies the flat formula on its own.

Holding the nominal annual rate constant, compounding more often produces a larger result, because interest begins earning interest sooner. ₹1,00,000 at a nominal 10% for 10 years:

Read the third column before the fourth. The effective annual rate is what a nominal 10% actually delivers once the frequency has done its work: 10% flat annually, 10.47% compounded monthly, 10.52% compounded daily. That is the whole effect, and the future value column is just the same fact after ten years.

Two cautions. First, this comparison only works because the nominal rate is being held constant — a product quoting an effective rate has already absorbed its own frequency, and comparing two products on nominal rates without checking their conventions is precisely the error this table exists to expose. Second, nothing here implies that any financial product actually compounds at any of these frequencies. They are options in a calculator, not a description of the market.

The gains also shrink fast. Going from annual to monthly adds ₹11,330 over ten years; going from monthly to daily adds ₹1,087. The ceiling is continuous compounding, A = Pe^(rt), which gives ₹2,71,828 — only ₹37 more than daily. Beyond a point, frequency stops mattering.

Adding money regularly changes the shape of the result. Each contribution starts earning from the date it arrives, so early contributions do far more work than late ones — and over a long term the contributions usually contribute more than the opening amount, simply because there are so many of them.

₹1,00,000 at an assumed 10% compounded monthly over 15 years reaches ₹4.45 lakh on its own. Adding ₹5,000 a month takes it to ₹25.18 lakh:

1Principal                    ₹1,00,0002Contributions (180 × ₹5,000) ₹9,00,0003Total contributed            ₹10,00,0004Estimated interest           ₹15,17,7445Estimated future value       ₹25,17,7446 7More than half the final figure is interest,8and most of that interest is on the contributions9rather than on the opening amount.

The timing convention matters and is stated rather than hidden. This calculator assumes contributions are made at the end of each period by default — the money arrives at the close of the month and earns nothing that month. That is the standard recurring-contribution convention and the one the published annuity formula encodes. You can switch to beginning-of-period, which buys every contribution one extra period of growth; on the example above that is worth ₹17,270.

The schedule is built contribution by contribution rather than approximated with a multiplication. That matters most when the contribution frequency and the compounding frequency differ — annual compounding with monthly contributions, for instance — where a shortcut formula quietly stops being right.

Daily compounding means n = 365: the rate is divided by 365 and applied that many times a year. On ₹1,00,000 at a nominal 10% over 10 years it produces ₹2,71,791, against ₹2,59,374 compounded annually. The effective annual rate is 10.52%.

It is the most frequent option here, and it sits very close to the theoretical ceiling — continuous compounding gives ₹2,71,828, a difference of ₹37 over a decade.

Be careful reading this as a product claim. Some savings accounts calculate interest on daily balances but credit it quarterly, which is not the same thing as daily compounding. Many products do not work this way at all. The option here controls this calculator’s arithmetic; what any particular account does is set out in its own terms.

Monthly compounding means n = 12. Each month applies one twelfth of the nominal annual rate, and because each month’s interest then earns interest itself, a nominal 10% compounds to an effective 10.47% over a year.

On ₹1,00,000 over 10 years that is ₹2,70,704 against ₹2,59,374 compounded annually — a difference of ₹11,330 from the frequency alone.

Monthly is the most common convention in calculators aimed at investment planning, largely because monthly contributions are common and it lines the two up neatly. If you are comparing this calculator’s output against another one and the figures differ slightly, the compounding frequency is the first thing to check.

Annual compounding means n = 1, and the formula reduces to A = P(1 + r)^t. Interest is calculated once a year and added to the balance. It is the simplest convention, the easiest to check by hand, and this calculator’s default.

With annual compounding the nominal and effective rates are the same number, which makes it the cleanest baseline for comparing against anything else. ₹1,00,000 at 10% grows like this:

Notice the shape. The first decade adds ₹1.59 lakh and the second adds ₹4.13 lakh — more than two and a half times as much, from the same principal at the same rate. That asymmetry is the most useful thing a long projection has to show, and it is the reason duration is worth more attention than the rate for anyone with time available.

₹1,00,000 is the calculator’s default and the figure most people try first. At an assumed 10% compounded annually it is ₹2,59,374 after 10 years and ₹6.73 lakh after 20. At an assumed 12% compounded monthly, 10 years gives ₹3.3 lakh.

The way to use the tool is to move one input at a time and watch what happens. Change the rate from 10% to 12% and the ten-year figure moves by about ₹51,000; change the duration from 10 years to 20 and it moves by more than ₹4 lakh. That comparison — which input the answer is actually sensitive to — is worth more than any single number the calculator produces.

None of these figures is a return anyone is offering. They are what the arithmetic gives for the assumptions entered, and the assumptions are yours.

₹5,00,000 at an assumed 10% compounded annually reaches ₹20.89 lakh over 15 years, of which ₹15.89 lakh is interest.

Because the calculation is exactly proportional to the principal, ₹5 lakh always produces five times what ₹1 lakh produces on identical assumptions — no exceptions, at any rate, frequency or duration. That makes it a useful sanity check on any compound interest figure you are shown anywhere: scale it down to ₹1 lakh in your head and see whether it still looks right.

The Principal comparison in the calculator runs ₹10,000 through to ₹10,00,000 side by side at whatever rate and duration you have set, which shows the proportionality directly.

₹10,00,000 at an assumed 12% compounded monthly reaches ₹1.09 crore over 20 years. At an assumed 10% compounded annually the same amount over the same period reaches ₹67.27 lakh — the two-percentage-point difference and the frequency together account for a gap of more than ₹40 lakh.

At this scale the sensitivity to the rate assumption is worth dwelling on. The Interest rate comparison runs 6%, 8%, 10%, 12% and 15% side by side; over twenty years the spread between the top and bottom rows is usually large enough that no decision resting on the middle row is safe. That spread is the honest output of this kind of calculation — a single figure quoted without it says less than it appears to.

There are two answers, and they are not the same answer.

The exact calculation inverts the compound interest formula:

1t = ln(2) / [n × ln(1 + r/n)]2 3At 10% compounded annually:4t = 0.6931 / ln(1.1) = 7.27 years5 6At 10% compounded monthly:7t = 0.6931 / [12 × ln(1.008333)] = 6.96 years

The Rule of 72 is the mental shortcut: divide 72 by the rate. At 10% that gives 7.2 years, which is close to the exact 7.27. At 8% it gives exactly 9 years against an exact 9.01 — out by about three days.

The rule drifts as you move away from 8%, overstating at low rates and understating at high ones. The calculator shows both figures side by side, with the error in years, and uses the exact one for everything it computes. A rule of thumb is useful in your head; it is not what a calculator should be doing.

An approximation for doubling time that needs no calculator:

1Doubling time (years)  ≈  72 / interest rate2 3At  4%   72 / 4  = 18 years    (exact 17.67)4At  6%   72 / 6  = 12 years    (exact 11.90)5At  8%   72 / 8  =  9 years    (exact  9.01)6At 10%   72 / 10 = 7.2 years   (exact  7.27)7At 12%   72 / 12 =  6 years    (exact  6.12)8At 20%   72 / 20 = 3.6 years   (exact  3.80)

It works because ln(2) ÷ ln(1 + r) happens to be close to 0.72 ÷ r for small rates, and 72 divides neatly by a lot of common percentages. The accuracy is best around 8% and degrades in both directions — noticeably so above 15%.

Use it to sanity-check a figure in your head, not to produce one. It is a rough estimation and not the compound interest calculation, and this calculator never uses it as the primary formula.

A projection tells you the balance. It does not tell you what that balance will buy. Those are different questions and this calculator keeps them as two separate figures rather than blending them into one.

1Real Value = Future Amount / (1 + inflation)^years2 3₹10,00,000 in 20 years, 6% inflation:4₹10,00,000 / (1.06)^20 = ₹3,11,8055 6The nominal balance is ₹10 lakh.7Its purchasing power is about ₹3.12 lakh in today's money —8roughly 31% of the figure on the screen.

The related figure is the real rate of return, and it is calculated by division rather than subtraction:

1Real Return = ((1 + nominal) / (1 + inflation)) - 12 310% nominal against 6% inflation:4(1.10 / 1.06) - 1 = 3.77%5 6Not 10 - 6 = 4%.7 8The naive subtraction overstates by 0.23 percentage points9here, which looks trivial over one year and is not10trivial at all once it compounds over twenty.

The Inflation tab in the calculator does both adjustments and reports the nominal and real figures side by side. Neither is mixed into the headline, because a number that quietly blends the two is neither the balance you would see nor the value in today’s money.

Compound growth calculations are commonly used to illustrate what an investment might do. That is a legitimate use, provided the difference between an illustration and a projection stays visible.

Four things are true of every investment figure on this page:

• Actual investment returns vary. The calculator applies one rate to every period. No investment has ever behaved that way for a single year, let alone twenty.
• Market-linked returns are not fixed. Equity and equity-oriented funds can fall, and can stay down for years. A projection that only goes up is a property of the arithmetic, not of the asset.
• Taxes and fees reduce what you actually receive. Nothing here accounts for either. Both compound too, in the wrong direction.
• Past performance does not guarantee future performance. A historical return is a reasonable place to start an assumption and is not a prediction of anything.

The useful thing a calculator like this can do for an investment decision is not to produce a number. It is to show how much the number moves when the assumption moves — which is what the rate comparison is for.

For savings the arithmetic is on firmer ground, because a stated savings rate is usually an actual rate rather than an assumption about the future. The projection still depends on the rate staying where it is, which for most savings products it does not — rates move.

The pattern worth seeing here is what a regular contribution does. Savings balances are usually built from monthly additions rather than a single deposit, and the contribution schedule tends to dominate the interest over shorter horizons: over five years at a typical savings rate, most of the final balance is money you put in. Over twenty-five years the proportions reverse.

This page does not quote current savings rates for any bank or product, because those change and a figure written into a calculator would be wrong within months. Use the rate your own account actually pays.

A fixed deposit is the case compound interest arithmetic fits best: a known amount, a contractually fixed rate, a fixed term. If you enter the rate and the compounding convention from the deposit’s own terms, the projection should be close to what the bank quotes.

Three things vary by institution and product, and none of them can be assumed:

• The compounding convention. Quarterly is common for term deposits in India, but it is not universal and it is not guaranteed for any particular product.
• Whether interest is compounded or paid out. A cumulative deposit compounds; a non-cumulative one pays interest periodically and does not, which makes it a simple-interest calculation.
• The rate. Deposit rates differ between institutions, between tenures and over time, and are frequently different again for senior citizens.

Deposit interest is also generally taxable as income, and nothing on this page accounts for that. The terms of the specific product are what govern the account — this calculator applies a clean formula to whatever assumptions you enter.

These are the same arithmetic pointed in opposite directions, and the two words are often used as if they were interchangeable.

Concretely: if ₹1,00,000 became ₹2,59,374 over 10 years, the CAGR is 10% — exactly the rate that would have produced that figure under annual compounding. Compound interest projects forwards from a rate; CAGR reads a rate backwards from a result.

The one thing CAGR does not tell you is what happened in between. Two investments with an identical CAGR can have had wildly different paths, and one of them may have been unholdable. The concepts are related, not identical. If you already have a start value, an end value and a number of years, the CAGR calculator reads the rate out of them directly.

A SIP — Systematic Investment Plan — is not a product and not a calculation. It is a standing instruction to invest a fixed amount at a fixed interval, usually monthly, into a mutual fund scheme. The SIP is the instruction; the fund is what holds the money and determines what happens to it.

Compound interest is the growth model. A SIP calculator applies an assumed compound growth rate to a stream of contributions — which is exactly what this calculator does when you switch monthly contributions on. The arithmetic is the same arithmetic.

What differs is how much weight the assumed rate can carry. For a fixed deposit the rate is contractual. For a market-linked fund it is a guess about the future, and actual returns depend entirely on the underlying investment. The SIP calculator is built around that case specifically, with a step-up schedule and goal planning; this one is built around the general compound interest question.

• Using the rate as a percentage instead of a decimal. The formula needs 0.1, not 10. Getting this wrong does not produce a slightly wrong answer; it produces an absurd one.
• Forgetting the compounding frequency. The same nominal rate produces different answers at different frequencies, and comparing two figures computed on different conventions compares nothing.
• Using the wrong duration. t is in years. A term entered in months without conversion is out by a factor of twelve.
• Confusing interest with future value. A is the total; the compound interest is A − P. Quoting the future value as the interest earned overstates it by the entire principal.
• Ignoring contribution timing. Beginning-of-period and end-of-period contributions differ by one period of growth on every payment. Small per payment, not small in total.
• Treating an assumed rate as a guaranteed one. The most consequential mistake on this list. The rate is an input you chose, and every figure downstream inherits whatever is wrong with it.
• Ignoring inflation.A balance twenty years out is quoted in money that will buy less than today’s. Nominal growth and purchasing power are different measurements.
• Ignoring fees and taxes. Both reduce what you actually receive, and both compound.
• Rounding too early. Rounding the rate or an intermediate balance and then compounding it for twenty years amplifies the error every period. Round for display, never during the calculation.

• Savings planning
• Investment projections
• Education planning
• Retirement planning
• Long-term wealth illustrations
• Fixed deposit calculations
• Understanding how interest accumulates
• Financial goal planning

Whether any of these is appropriate for you depends on your own circumstances — your income, your obligations, your tax position, your time horizon and your tolerance for a balance that falls. A calculator knows none of that. It compares scenarios; it does not recommend one.