Compound Interest Calculator
Compound interest means earning returns on returns. The formula is straightforward; what is genuinely hard to hold in your head is how non-linear the result is, which is why the same rate over 40 years produces a result several times larger than over 20.
How to use it
- Enter your starting principal, annual rate, and number of years.
- Set the compounding frequency, defaulting to monthly.
- Read the future value and total interest earned.
Growth is exponential, and intuition is linear
The formula multiplies the principal by one plus the periodic rate, raised to the number of periods. Because the exponent is the number of periods, adding years does not add to the result proportionally — it multiplies it.
The clearest demonstration is doubling time, and the rule of 72 gives it approximately: divide 72 by the percentage rate. At 8 percent money doubles roughly every nine years. So $10,000 becomes $20,000 in nine years, $40,000 in eighteen, $80,000 in twenty-seven, and $160,000 in thirty-six. The final doubling adds $80,000 — more than every prior period combined.
That structure is why starting early beats contributing more, and by a wide margin. $10,000 invested at 8 percent at age 25 reaches about $217,000 by 65. The same $10,000 invested at 35 reaches about $100,000. Ten years of delay costs more than half the outcome, and no realistic increase in contribution makes it up.
Compounding frequency, and why it matters less than expected
More frequent compounding produces slightly more growth, because interest starts earning sooner. The effect is real but small, and it is smaller than most people assume.
On $10,000 at 6 percent for ten years: annual compounding gives $17,908; monthly gives $18,194; daily gives $18,220. Continuous compounding, the theoretical limit, gives $18,221. The jump from annual to monthly is worth $286 over a decade; everything beyond monthly is worth $27.
This is where the distinction between nominal and effective rates comes in. A 6 percent nominal rate compounded monthly has an effective annual rate of about 6.17 percent, and that is the number to compare across products. Regulated disclosures exist for this reason: APY on deposits and APR on loans are meant to be comparable figures. When two products quote different compounding, comparing nominal rates is comparing nothing.
What this projection does not account for
The output is a clean mathematical projection. Three things reliably make real outcomes lower, and ignoring them produces badly misleading numbers.
- Inflation. At 3 percent, money loses about half its purchasing power over 24 years. A projection showing $100,000 in 30 years is worth roughly $41,000 in today terms. Subtracting the inflation rate from your return rate gives a real figure that is far more useful for planning.
- Fees. An expense ratio compounds against you exactly as returns compound for you. One percent annually on a 40-year horizon typically removes 20 to 25 percent of the final balance — not 1 percent, because you lose the growth on every dollar of fee as well.
- Tax. Interest and dividends in a taxable account are taxed as received, so the amount compounding is the after-tax amount. Tax-advantaged accounts avoid this drag, which is a large part of why they outperform an identical portfolio held taxably.
- Volatility. This model assumes a constant rate. Real returns vary, and the sequence matters when you are withdrawing rather than accumulating: poor returns early in retirement do considerably more damage than the same returns later, even at an identical average.
Regular contributions
This tool projects a single lump sum. Most saving is periodic, which behaves differently: each contribution compounds only for its remaining time, so a dollar added in year one does far more work than a dollar added in year 29.
The practical consequence is that contribution timing within a plan matters much less than the total years the plan runs. Front-loading contributions helps, but the dominant variable remains how long the money has, which is another way of saying the same thing as the age comparison above.
At a glance
| Formula | A = P(1 + r/n)^(nt) |
|---|---|
| Compounding | Any periods per year, defaults to monthly |
| Excludes | Inflation, fees, tax, and volatility |
| Transmitted | Nothing |
Frequently asked questions
How long until my money doubles?
Divide 72 by the percentage rate for a close approximation. At 8 percent that is about nine years, at 6 percent about twelve.
Does daily compounding beat monthly?
Barely. On $10,000 at 6 percent over ten years, daily gives $18,220 against $18,194 monthly. The annual-to-monthly step matters far more than anything beyond it.
Should I adjust for inflation?
Yes, for any long horizon. Subtract the inflation rate from your return rate to get a real figure. At 3 percent inflation, purchasing power halves in about 24 years.
How much do fees really cost?
A 1 percent annual fee typically removes 20 to 25 percent of a 40-year balance, because you lose the compounded growth on every dollar taken as well as the dollar itself.
Read more
How loans actually work — Why your first payment is almost all interest, and why the term costs more than the rate.