Compound Interest Calculator
Compound interest is interest earned on both your original money and the interest it has already earned, so your balance grows faster the longer you leave it. Enter your amount, rate and term to see the future value, total interest and APY.
See how your savings or investments grow with compound interest — in any currency, with optional regular deposits or withdrawals and compounding from daily to yearly. Model a savings plan or a retirement drawdown and see the future value, total interest, effective APY, how long your savings last, and a full year-by-year breakdown. A second tab converts a rate between compounding frequencies (APR ↔ APY).
Works worldwide — pick your currency and enter your own figures. Educational estimate, not financial advice.
Fill in the details and press Calculate. Changing a dropdown updates the result automatically.
Year-by-year breakdown
How compound growth works
Compound interest is interest earned on your interest. Each period, the interest you have already earned is added to the balance, so the next lot of interest is worked out on a bigger number. Over years, that turns a straight line into a curve that bends upward — the famous snowball effect.
Say you put 10,000 away at a fixed 5% a year with yearly compounding. Year one adds 500; year two earns 5% on 10,500 (not just the original 10,000), so 525; year three earns on 11,025, and so on. After 20 years the balance is about 26,533 — more than 2.5× your money, with over 16,500 of it pure interest. Switch on regular deposits and the curve steepens sharply.
Here it is in numbers — the same 1,000 at 5% a year, worked out two ways. Simple interest pays 5% only on your original 1,000 each year; compound interest pays 5% on the whole growing balance:
| After… | Simple interest | Compound interest |
|---|---|---|
| 1 year | 1,050.00 | 1,050.00 |
| 2 years | 1,100.00 | 1,102.50 |
| 3 years | 1,150.00 | 1,157.63 |
| 5 years | 1,250.00 | 1,276.28 |
| 10 years | 1,500.00 | 1,628.89 |
| 20 years | 2,000.00 | 2,653.30 |
They start level, but by year 20 compounding is 653 ahead on the very same rate — and the gap widens every year after. That widening gap is the whole point of compounding:
Real savings rates and investment returns change over time, so treat any single-rate projection as a guide, not a guarantee.
Three ways to grow it faster
- Start early. Time is the biggest lever in compounding — money invested in your twenties can out-grow much larger sums added later, simply because it compounds for longer.
- Add to it regularly. Steady deposits — weekly, monthly, whatever suits — feed the snowball. Each new deposit starts earning its own interest, and the optional yearly-increase box lets you grow those deposits with your income.
- Mind the compounding frequency. The more often interest is added, the higher your real yield (APY). The jump from yearly to monthly matters most; beyond daily the gains are tiny.
Model all three with the tabs above, then read the effective APY the calculator reports to compare accounts fairly.
How long will my savings last?
Set Add or withdraw? to Regular withdrawals and the tool becomes a retirement drawdown calculator: enter your pot, the return you expect and the income you want to take, and it shows how long the money lasts before it runs out — or, if growth outpaces your withdrawals, how much is left at the end.
A common starting point is the 4% rule: taking about 4% of your pot in the first year, then rising with inflation, has historically lasted roughly 30 years. Use the Withdrawal yearly increase box to keep your income moving with prices, and try a rate a point higher or lower — you will see how much a single percentage point on either the return or the withdrawal shifts the “runs out” date.
A projection, not financial advice. Real returns vary year to year, so leave a margin and review your plan regularly.
Where you earn compound interest
Most savings and investment products compound — this calculator works for any of them, so just enter the rate and how often it compounds:
- Savings & money market accounts — usually compound daily or monthly. Enter the account’s APY, or its nominal rate with the matching frequency.
- Certificates of deposit (CDs) and fixed-rate bonds — a set rate for a fixed term; leave deposits off to model a single lump sum.
- Investments, ISAs, Roth IRAs and 401(k)s — use your expected annual return. The account wrapper changes the tax, not the compounding maths, so this projects the growth — not the contribution limits or tax rules.
Compound interest also works against you on debt such as credit cards. To pay money back rather than grow it, use our debt payoff calculator or loan calculators instead.
APR vs APY, and the rate converter
The Rate converter tab translates a rate between compounding frequencies. APR is the plain nominal rate and ignores in-year compounding; APY (the effective annual rate) folds it in, so it reflects what you truly earn. For example, 6% compounded monthly equals 6.16778% annually. Banks often quote APY on savings and APR on loans, so converting to a common basis is the only fair way to compare offers.
6% nominal at every frequency
The same 6% rate, shown at each compounding frequency, with the rate it works out to per period and the equivalent annual yield (APY):
| Compounded | Rate per period | Equivalent APY |
|---|---|---|
| Annually | 6% | 6% |
| Semiannually | 3% | 6.09% |
| Quarterly | 1.5% | 6.13636% |
| Monthly | 0.5% | 6.16778% |
| Semimonthly | 0.25% | 6.1757% |
| Biweekly | 0.23077% | 6.17632% |
| Weekly | 0.11538% | 6.17998% |
| Daily | 0.01644% | 6.18313% |
| Continuously | — | 6.18365% |
Each step up in frequency adds less than the one before, closing in on the 6.18365% continuous ceiling.
How to use it & key terms
Enter your starting amount, rate, compounding frequency and time, add optional deposits or withdrawals, then press Calculate for the future value, total interest and APY.
| Term | What it means |
|---|---|
| Principal | Your starting amount. |
| Compound interest | Interest earned on both your money and the interest it has already earned. |
| Compounding frequency | How often interest is added (daily to yearly); more often earns a little more. |
| APY | The effective annual rate once compounding is counted — the true yearly yield. |
| Future value | Your projected balance at the end. |
| Contribution | A regular deposit that feeds the growth; it can rise each year. |
| Time to double | How long your money takes to double at the effective rate. |
Sources & methodology
CalcCopilot builds the projection period by period, the way a real statement grows: each period we add the interest earned on the running balance, apply any deposit or withdrawal on its own schedule, then let that interest join the balance at each compounding point so it starts earning too. Deposits and withdrawals can each rise a set percentage a year, withdrawals stop at zero (your money never goes below empty), and the year-by-year table lays out every step. The effective annual rate (APY) comes from your nominal rate and compounding frequency, and drives the “time to double” figure.
The formulas behind it
| Quantity | Formula |
|---|---|
| Future value of the initial amount | A = P × (1 + r÷n)n·t |
| Effective annual rate (APY) | APY = (1 + r÷n)n − 1 |
| Future value of regular deposits | FV = PMT × [ ((1 + j)N − 1) ÷ j ] |
| Time to double | t = ln(2) ÷ ln(1 + APY) |
Here P is the initial amount, r the annual rate, n the compounds per year, t the years, PMT each deposit, j the per-deposit-period rate derived from the APY, and N the number of deposits.
Read in plain English: the first line says your lump sum multiplies by the compounded rate; the annuity line totals every deposit and the interest each one goes on to earn; and a withdrawal is simply a negative deposit on the same timeline — so one set of maths tells you both how a pot grows and how long it lasts once you start drawing on it. The same compounding powers real-life plans: point it at a target with the savings goal calculator, or at a nest egg you'll draw down with the retirement calculator.
Worked example — 5,000 at 5%, compounded monthly, 5 years, no deposits:
APY = (1 + 0.05/12)^12 − 1 = 5.11619%
A = 5000 × (1 + 0.05/12)^(12×5) = 6,416.79
interest = 6,416.79 − 5,000 = 1,416.79 · growth = 28.34%
With deposits — 10,000 at 5% (yearly compounding) plus 100 a month for one year:
interest = 10,000 × 5% ÷ 12, summed across the 12 growing monthly balances = 527.50
balance = 10,000 + (12 × 100 in deposits) + 527.50 = 11,727.50
every figure ships checked to the cent against the period-by-period statement — the CalcCopilot way.
Method & sources: standard compound-interest, future-value-of-an-annuity and effective-annual-rate formulas, run as a period-by-period simulation and checked to the cent against worked examples.
The Rule of 72 and the shape of the curve
Compound growth has a distinctive shape that catches almost everyone off guard: it starts out looking disappointingly flat, then bends sharply upward the longer it runs. In the early years the interest is small because the balance is small, and it is easy to feel like nothing is happening. But each bit of interest joins the balance and starts earning its own interest, so the curve steepens — and most of the dramatic growth arrives late, in the final stretch of a long timeline. Give up early and you quit right before the part that makes compounding worth the wait.
A handy shortcut for picturing this is the Rule of 72. Divide 72 by your annual rate and you get a rough number of years for your money to double. At 6% a year, money doubles in roughly twelve years; at 8%, in about nine. The rule is only an approximation, but it is close enough for quick mental maths and it makes the effect of a higher rate vivid: a couple of extra percentage points can turn three doublings over a lifetime into four, and each doubling is larger than all the previous growth combined.
The same arithmetic exposes the real cost of waiting. Because the biggest gains come at the end, the years you delay are the most expensive ones you can lose — you are not shaving time off the flat beginning, you are cutting off the steep end. A sum invested several years earlier can finish well ahead of a larger sum invested later, simply because it was handed more doublings. This is why starting is so often more powerful than optimising: a modest amount put to work today usually beats a perfect plan that begins next year.
None of this depends on dramatic returns or clever timing. It rewards patience, consistency, and leaving the balance alone so the interest can keep stacking. The practical takeaways are plain: begin as soon as you reasonably can, resist the urge to dip into the pot, and let time do the heavy lifting rather than chasing a spectacular rate. Compounding is not a trick to master so much as a force to respect — quiet and unremarkable for years, then surprisingly powerful once it has had enough time to run.
Frequently asked questions
What does this compound interest calculator do?
It shows how a starting amount plus optional regular deposits grow over time with compound interest, in any currency. It reports the future value, total interest, effective APY, time to double and a year-by-year breakdown, and a second tab converts a rate between compounding frequencies.
Can I use it in my own currency?
Yes. Choose from US dollars, pounds, euros, rupees, yen, Australian and Canadian dollars, yuan, rubles and more. The symbol is only a label — the maths is identical everywhere in the world.
How is compound interest calculated?
The initial amount uses A = P(1 + r÷n)n·t. Regular deposits use the future-value-of-an-annuity formula. Interest compounds at the frequency you choose, from daily to yearly.
Can I include regular deposits?
Yes. Enter a deposit amount and how often you add it (weekly to yearly), and optionally raise it by a set percentage each year to match pay rises or inflation.
What is APY, the effective annual rate?
APY is the true yearly yield once compounding is counted. For example, 5% compounded monthly is 5.12% APY. The calculator shows it so you can compare accounts fairly.
Does the compounding frequency change my result?
Yes, a little. More frequent compounding earns slightly more for the same nominal rate, and the effect grows with the rate. Going from yearly to monthly matters most.
What does “time to double” mean?
It is how long your initial amount takes to double at the effective rate, using t = ln(2) ÷ ln(1 + APY). The Rule of 72 is a rough shortcut; this uses the exact figure.
Is this for savings or investments?
Both. Enter a fixed savings rate, or the annual return you expect on an investment. Remember real investment returns vary year to year, unlike a fixed savings rate.
What is the difference between APR and APY?
APR is the nominal rate and ignores in-year compounding; APY includes it. APY is therefore higher than APR whenever interest compounds more than once a year.
Does 10% compounded semiannually equal 10.25% a year?
Yes. Half of the 10% is credited after six months, then the second half-year earns interest on that too, lifting the full-year figure to 10.25%.
How do I calculate daily compound interest?
Set Compounding to Daily: the balance grows by A = P(1 + r÷365)365·t. For example, 5% compounded daily is an effective 5.13% a year — a touch more than monthly. Add a deposit to include regular saving.
What is cumulative or accrued interest?
It is the running total of interest earned so far. In the year-by-year breakdown, the Interest column added up to any point is your accrued (cumulative) interest, and it climbs faster each year as compounding builds.
Does a Roth IRA, 401(k) or ISA earn compound interest?
Yes — the investments inside them compound like any other. This tool models that growth from your expected return; it does not apply account-specific contribution limits or tax rules, so treat it as the compounding maths, not tax advice.
What is the compound interest formula?
A = P(1 + r÷n)n·t, where P is the principal, r the annual rate, n the times it compounds per year and t the years. Regular deposits add a future-value-of-an-annuity term, and continuous compounding uses A = Pert.
Is this a CAGR calculator?
Related, but reversed. CAGR works out the annual growth rate from a starting and ending value; this calculator projects an ending balance forward from a rate. The effective APY and time-weighted return it reports are the compound growth rate for your inputs.
How much interest does $1 million earn in a year?
It depends on the rate. At 5% a year, $1,000,000 earns about $50,000 simple, or ~$51,162 compounded monthly. At 4% it's ~$40,000 and at 6% ~$60,000. Enter $1,000,000, your rate and one year above to see the exact figure and how it grows if you keep compounding.
Is this financial advice?
No. It is an educational estimate to help you plan. Savings rates and investment returns can change, so confirm figures with your provider before making decisions.