Projection
Runs locallyGrowth over time
The shaded area between the lines is the interest you earned.
Ready.
Year-by-year breakdown
The table below is the same calculation the chart uses — one row per year, so you can see exactly when the growth accelerates and check the final figure against the summary above.
| Year | Contributions | Interest | Balance |
|---|
The formula
Compound interest combines two things: growth of the initial lump sum, and growth of the monthly contributions. Both use the same effective monthly rate, which is derived from the nominal annual rate and the compounding frequency you selected.
Effective annual rate = (1 + nominal_rate ÷ n)^n − 1 Effective monthly rate = (1 + effective_annual_rate)^(1/12) − 1 Future value = P × (1 + r_m)^(12t) + PMT × [(1 + r_m)^(12t) − 1] ÷ r_m Where: P = initial lump sum PMT = monthly contribution r_m = effective monthly rate t = number of years n = compounding periods per year
Once the effective monthly rate is known, both the lump sum and the contributions use the same exponent. The contributions are a standard annuity: the same deposit at the end of every month, accumulated at the monthly rate. The formula for that sum is the geometric series in the bracket.
Why compounding frequency matters
More frequent compounding produces a slightly higher effective annual return, because each interest payment is added to the balance sooner and starts earning interest sooner. The difference is small per year but compounds over decades.
| Frequency | Formula | Effective annual rate |
|---|---|---|
| Annually | (1 + 0.07/1)^1 − 1 | 7.000% |
| Quarterly | (1 + 0.07/4)^4 − 1 | 7.186% |
| Monthly | (1 + 0.07/12)^12 − 1 | 7.229% |
| Daily | (1 + 0.07/365)^365 − 1 | 7.250% |
| Continuous | e^0.07 − 1 | 7.251% |
On $10,000 held for 30 years at 7%, annual compounding produces $76,123, and daily compounding produces $76,255. The 30-year difference is $132 on a $10,000 investment — less than most people expect, because the intra-year frequency compounds on a very small base. Compounding frequency matters far more when the rate is high, and it matters least when it is low.
What matters more than frequency: the rate itself, and the number of years. Doubling the rate roughly quadruples the final balance over long periods. Doubling the years roughly doubles the balance at modest rates and much more than doubles it at high rates. If you want to prioritise one variable to maximize the outcome, prioritise the years.
APR versus APY
One of the most common sources of confusion in savings calculators is entering the wrong rate. Banks advertise two different numbers, and they are not the same thing.
APR — Annual Percentage Rate
The nominal rate, before any intra-year compounding. If a savings account says "7% APR compounded monthly", the nominal rate is 7% and the compounding frequency is monthly. Enter both of those numbers into this calculator and you get the correct answer.
APY — Annual Percentage Yield
The effective annual rate, after compounding is included. If an account says "7.23% APY", the bank has already done the compounding math for you. To match that number, you either:
- Enter 7.23 as the rate and set compounding to Annually — this makes the calculator's effective annual rate exactly 7.23%, or
- Enter the nominal rate (for example 7%) and set compounding to whatever the account actually uses (for example monthly). This is the more accurate approach if you know both numbers.
Real return after inflation
The future value this calculator shows is a nominal number. It tells you how many dollars you will have in thirty years, not what those dollars will be able to buy. For a rough estimate of real purchasing power, subtract the expected inflation rate from the nominal rate before entering it.
Rough real rate ≈ nominal rate − inflation rate Exact real rate = (1 + nominal) ÷ (1 + inflation) − 1
If you expect a 7% nominal return and 3% inflation, the rough arithmetic gives 4% real. The exact arithmetic gives (1.07 ÷ 1.03) − 1 ≈ 3.88%. At these numbers the difference between rough and exact is small. At higher numbers it matters more: 10% nominal with 7% inflation is roughly 3% real, but exactly (1.10 ÷ 1.07) − 1 ≈ 2.80%.
A 4% real return means your purchasing power roughly doubles every 18 years. A 2.8% real return takes about 25 years. That is the difference between a comfortable retirement and a tight one, and it is why the inflation assumption is often more consequential than the rate assumption.
Common mistakes
Using a projected rate as a guarantee
Every number in this calculator is a projection, not a forecast. A 7% return compounded for 30 years is arithmetically correct for a 7% return, but no investment delivers a steady 7% for 30 years. The stock market falls some years and rises others, and the order of those returns matters because it determines whether you are buying when prices are low or high.
Forgetting to adjust for tax
In a taxable account, interest and dividends are taxed as ordinary income in the year they accrue, which reduces the amount that compounds in the following year. This calculator does not model tax, and it does not model tax-advantaged accounts like a Roth IRA or an ISA that change the math significantly. For a rough approximation of a taxed account, reduce the rate by your marginal tax rate on interest income.
Comparing a taxable account to a tax-advantaged one
A 7% return in a Roth IRA is worth more than a 7% return in a taxable brokerage account, because the Roth compounds tax-free while the taxable account pays tax along the way. If you are choosing between accounts, the tax treatment is part of the return.
Assuming contributions are indexed to inflation
The calculator uses a fixed monthly contribution for the entire period. In real life, contributions tend to rise with income and inflation. If you want to model that, split the projection into two or three chunks with different contribution amounts and add the results — the calculation is additive across chunks when the years are contiguous.
Ignoring fees
A 1% annual fee on a 7% return reduces the effective return to about 6%. Over 30 years, that 1% costs about a fifth of the final balance. This calculator does not model fees, but it is easy to model them by subtracting the fee rate from the interest rate before entering it.
What this calculator does not do
- It does not model tax. All figures are pre-tax. Interest in a taxable account is taxed as it accrues; a retirement account is taxed on withdrawal (traditional) or not at all (Roth). Add or subtract the tax treatment to match your situation.
- It does not adjust for inflation. The number you see is a nominal figure. To see real purchasing power, subtract an inflation estimate from the rate before entering it.
- It does not model fees. Expense ratios, advisory fees, and account fees all reduce the effective rate. If you know your total fee, subtract it from the rate before entering it.
- It does not model changing rates. The rate you enter applies to every year of the projection. Real markets and real savings rates change over time.
- It does not model variable contributions. The monthly contribution is fixed. If your contribution will change, split the projection into chunks with different contribution amounts.
- It does not include an employer match. If you have a retirement account with a match, the effective contribution is higher than what you enter. Add the match to your monthly contribution field.
- It does not handle lump-sum withdrawals. The projection assumes you only add money. If you plan to withdraw at some point, the projected figure is the balance before the withdrawal.
- It does not predict what an investment will return. The rate you enter is your assumption. The calculator is exact arithmetic on that assumption, not a forecast.
Frequently asked questions
What is compound interest?
Compound interest is interest calculated on both the original principal and on interest that has already been added to the balance. Simple interest only pays on the principal, so the same rate produces a straight line. Compound interest produces a curve that steepens over time, because each period's interest is added to the base on which the next period's interest is calculated.
How does compounding frequency affect growth?
More frequent compounding produces a slightly higher effective annual return, because interest is added to the balance sooner and starts earning interest sooner. At 7%, monthly compounding produces an effective annual rate of about 7.23%, while annual compounding produces exactly 7.00%. The difference is small per year but compounds over decades, and it is why lenders are required to disclose the APY rather than just the nominal rate.
Can I include regular contributions?
Yes. The Monthly contribution field adds a fixed deposit at the end of every month. The interest rate is converted to an effective monthly rate that reflects the compounding frequency you selected, so a monthly deposit earns interest from the month it is made rather than waiting until the end of the year. This matters most for annual or quarterly compounding, where the naive approach of depositing once per compounding period would understate the result by several hundred dollars over ten years.
Is my financial data secure?
No data you enter ever leaves the browser. Every calculation runs in JavaScript on your device. There is no API call and no analytics event containing your figures. You can confirm this in the Network tab: change a number, watch the chart redraw, and check that no request appears. The page also works with the network disconnected after it loads.
Why does the growth chart show two lines?
The lower line shows the total amount you have contributed — the initial lump sum plus every monthly deposit, with no interest. The upper line shows the future value with interest compounded on top. The gap between the two lines is the interest you have earned, and it is the clearest way to see compounding visually: the gap is narrow in the early years and widens dramatically in the later ones.
Is this calculator accurate for real-world savings accounts?
It is arithmetically correct for the inputs you give it. Whether it matches your actual account depends on the inputs. Real savings accounts often quote an APY (annual percentage yield) rather than a nominal rate, and if you enter the APY as the interest rate the calculator will overstate the result slightly, because it will treat the APY as a nominal rate and compound it monthly on top. To match a stated APY, enter it and set compounding to Annually. To match a stated nominal APR, enter that and use the account's actual compounding frequency.
Does the calculator account for inflation or taxes?
No. It shows the nominal future value, before taxes on interest and before any inflation adjustment. Both reduce the real purchasing power of the result. For a savings account, interest is typically taxed as ordinary income in the year it accrues. For a retirement account, the tax treatment depends on whether it is pre-tax (traditional) or post-tax (Roth). If you want to see real returns, subtract the expected inflation rate from the nominal rate before entering it — a 7% return with 3% inflation is roughly 4% real, though the exact arithmetic is (1.07 ÷ 1.03) − 1 ≈ 3.88%.
What is the difference between this calculator and the retirement calculator?
This calculator projects the growth of a single pot of savings over a fixed number of years. The retirement calculator is a broader projection that models a working career followed by a withdrawal phase, accounts for contributions that change over time, and estimates whether your savings will last through retirement. Use this one to understand how compounding works and to size a specific goal; use the retirement calculator for a whole-career plan.
Why does the yearly breakdown stop at my end year?
The table shows one row per year for the duration you entered. If you set years to 30, you get 30 rows. The chart and the table use the same calculation, so the future value in the last row of the table is exactly the number shown in the result box. This is deliberate — it lets you verify that the chart and the summary figures agree.
Does a longer time horizon always mean more money?
For a fixed positive interest rate and fixed contributions, yes — the future value is monotonically increasing with time. But longer horizons also expose the result to more uncertainty: interest rates change, and the rate you enter is a projection rather than a guarantee. The later years of the chart are the most sensitive to that assumption, because that is where most of the compounding happens. A 30-year projection at 7% is not a forecast of what your account will hold in 2056; it is a projection of what it would hold if 7% held steady for 30 years, which no market does.
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