Compound Interest Calculator

How compound interest works

Compound interest is interest calculated on both your original balance and on the interest that balance has already earned. Each time interest is credited, it joins the balance, so the next calculation starts from a slightly larger number. Repeat that enough times and the curve stops looking like a straight line and starts climbing — that upward bend is the entire idea behind long-term saving and investing.

The formula behind this calculator is the standard lump-sum compound growth equation:

A = P × (1 + r/n)^{n × t}

Here A is the future balance, P is your starting principal, r is the nominal annual interest rate written as a decimal (5% becomes 0.05), n is how many times per year interest compounds, and t is the number of years. Total interest earned is simply the future balance minus everything you put in. When you add regular contributions, each deposit is treated as its own small principal that compounds for whatever time remains until the end of your term, and all of those amounts are summed alongside the original lump sum.

The effect of compounding frequency

Holding the nominal rate steady, compounding more often slightly increases your final balance. That seems counter-intuitive — the rate hasn't changed — but each compounding period applies a smaller slice of the annual rate (r ÷ n) more frequently, and interest on interest gets a head start sooner. Daily compounding will always edge out monthly, which edges out quarterly, which edges out annual, assuming the same nominal rate and time horizon. The differences are usually modest over short periods but become more noticeable as the rate climbs and the time horizon stretches into decades.

To make this concrete, here's how $10,000 at a 5% nominal annual rate grows over 10 years under each compounding frequency:

The gap between annual and daily compounding here is under $200 on $10,000 over 10 years — about 1.2%. That's also why the "effective annual growth" figure in your results can differ slightly from the nominal rate you typed in: it reflects the real one-year growth you'd experience once compounding is taken into account, the same idea behind a bank's quoted annual percentage yield (APY), though institutions may apply slightly different day-count conventions.

How to read your results

• Future balance — the total amount you're projected to have at the end of your time period, including your starting principal, every contribution you made along the way, and all interest earned.
• Total contributions — the sum of your initial principal plus every regular contribution, before any interest is added. This is "money you put in," not "money the math created."
• Total interest earned — the future balance minus your total contributions. This is the portion of your ending balance that compounding generated for you.
• Effective annual growth — an approximate single-year growth rate derived from how your balance grew relative to what you contributed, useful for comparing scenarios at a glance.
• Doubling time — both the quick Rule of 72 estimate (72 ÷ rate) and the exact number of years for your balance to double at your rate and compounding frequency, ignoring contributions.
• Year-by-year schedule — toggle it open to see how contributions, interest, and balance build year over year, which makes it easy to spot exactly when compounding starts pulling its own weight.

Real-world use cases

Compound interest calculator daily compounding 10 years

Set the compounding frequency to "Daily" and the time period to 10 years to model how a daily-compounding savings account or CD would grow. For example, $10,000 at 5% with daily compounding for 10 years grows to about $16,486.65 — only slightly more than monthly compounding's $16,470.09, illustrating how diminishing the gains from frequency become once you're already compounding often.

How much does $100,000 grow in 10 years at 8%?

Enter a principal of $100,000, a rate of 8%, and a time period of 10 years. With annual compounding, A = 100,000 × (1 + 0.08)¹⁰ ≈ $215,892 — more than double your starting balance, which lines up with the Rule of 72: 72 ÷ 8 = 9 years to double, and you've gone slightly past that mark at 10 years.

Compound vs. simple interest comparison

For the same $100,000 at 8% over 10 years, simple interest would only reach A = 100,000 × (1 + 0.08 × 10) = $180,000 — about $36,000 less than the compound result above. Run any plan through the Single Projection mode and check the "Compound vs. simple interest" chart to see this gap visualized for your own numbers.

Goal planning

Toggle the compounding frequency and contribution amount to see how small, steady changes — an extra $50 a month, a slightly higher rate, a longer horizon — ripple through the final balance. The scenario comparison table does this for you automatically, showing your plan against a daily-compounding version and a version with an extra $50/month contribution. That kind of side-by-side comparison is often more useful than chasing a single "right" number.

What a Good Result Looks Like

A healthy projection shows total interest earned growing to be a substantial share of your future balance — often 30% or more over long horizons — which means compounding, not just your own deposits, is doing real work. Your "Compound vs. simple interest" chart should show a visibly widening gap between the two lines over time, and your doubling time should roughly match what the Rule of 72 predicts for your rate.

Warning Signs in Your Results

Be cautious if: your "effective annual growth" is wildly different from your nominal rate (double-check whether large contributions are skewing the comparison); your time period is very short, making any compounding-frequency differences negligible and not worth optimizing for; or your rate assumption is unrealistically high for the asset class you're modeling — a 12%+ "guaranteed" rate over decades is not realistic for savings accounts or bonds.

How to Improve Your Result

The scenario comparison table shows two concrete levers: switching to daily compounding (usually a small gain) and adding $50/month in contributions (often a much larger gain over long horizons). In general, increasing your contribution rate or extending your time horizon will move the needle far more than chasing a slightly more frequent compounding schedule — use the "Compare Frequencies" mode to confirm how small that frequency effect really is for your numbers.