Compound Interest Calculator

How This Calculator Works

Compound interest is interest earned on interest: each period’s interest gets added to the balance, so the next period earns interest on a slightly larger amount. Over many years, that snowball effect can add up to more than the money originally put in.

Enter a starting amount, an annual interest rate, how many years you’ll let it grow, and an optional monthly contribution — this calculator shows what the account is worth at the end, split into how much of that came from your own contributions versus how much came from interest compounding on top of them.

By default the account compounds monthly, but you can change the compounding frequency (annually, semiannually, quarterly, monthly, or daily) to match a specific real account — more frequent compounding produces a very slightly higher return at the same stated annual rate, since interest starts earning its own interest sooner. You can also enter an assumed inflation rate to see the future value in today’s purchasing power, not just its nominal (unadjusted) dollar amount — the same real-vs-nominal distinction the Inflation Calculator uses.

The Formula

$$\text{FV} = \vA{P}(1+\vB{r})^{\vC{n}} + \vD{PMT} \times \frac{(1+\vB{r})^{\vC{n}} - 1}{\vB{r}}$$

where $\vA{P}$ is the starting principal, $\vB{r}$ is the monthly interest rate, $\vC{n}$ is the number of months (years × 12), and $\vD{PMT}$ is the monthly contribution.

When a compounding frequency other than monthly is chosen, $\vB{r}$ isn’t simply the annual rate divided by 12 — it’s derived in two steps so the math stays consistent regardless of how often interest actually compounds: first, the effective annual rate that frequency actually produces ($(1 + \text{rate}/\text{frequency})^{\text{frequency}} - 1$), then an equivalent monthly rate that would produce that same effective annual rate ($(1 + \text{effectiveAnnualRate})^{1/12} - 1$). Monthly contributions still happen every month regardless of compounding frequency, matching how people actually save (a paycheck-cadence habit) independent of the account’s own compounding schedule.

Worked Example

$10,000 to start, at 7% annual interest, over 10 years, with a $100 monthly contribution:

1. Monthly rate: $\vB{r} = 7\% \div 12 \approx 0.583\%$.
2. Number of months: $\vC{n} = 10 \times 12 = 120$.
3. Applying the formula gives a future value of about $37,405.

Of that, $22,000 was contributed directly (the $10,000 start plus $100 × 120 months), and roughly $15,405 came from compounding — money the account earned on its own, without any additional saving.

Common Mistakes

• Confusing a nominal annual rate with the effective annual rate. A 7% rate compounded monthly actually earns slightly more than 7% over a full year, since each month’s interest itself starts earning interest — the “effective” rate is the true annual return once that’s accounted for.
• Assuming a fixed rate holds for the entire projection. Real investment returns vary year to year; a single steady rate is a simplifying assumption for projecting forward, not a promise of what any specific year will actually return.
• Forgetting inflation erodes the real value of a future balance. $37,405 in 10 years won’t buy as much as $37,405 today — toggle “inflation-adjusted” above to see the projection in today’s purchasing power instead of nominal dollars.
• Ignoring taxes on interest earned. Interest in a regular (non-tax-advantaged) account is usually taxable in the year it’s earned, which reduces the real growth rate below what’s shown here unless the “tax on interest” field above is set to match your own situation.