Compound Interest
Growth projections plus ROI and CAGR
This tool has two modes, switchable by tab. Growth Projection is the forward version of the annuity arithmetic: give it a principal, a nominal annual rate, how often interest is credited, a number of years and an optional recurring deposit, and it reports the ending balance, total interest, the effective annual rate implied by that crediting frequency, and total return against the principal. Return / CAGR runs the arithmetic in reverse: give it a starting value, an ending value, and a time period, and it solves for the compound annual growth rate that connects them — useful for investments you can't cleanly model with a fixed periodic rate, like a stock position or a home's value.
The compounding-frequency selector in Growth Projection mode is the part worth understanding, because it is the part most people over-weight. At 8% on $10,000 for ten years, annual crediting ends at $21,589 and daily crediting ends at $22,253. The $664 gap is real — and it is under a third of what simply moving the rate from 8% to 9% is worth.
Calculations run in your browser. Projections are arithmetic on your assumptions, not investment advice.
Two terms, one compounding period
Balance = P x (1 + r/f)^(f x t) + D x ((1 + r/f)^(f x t) - 1) / (r/f)
P is the principal, r the nominal annual rate as a decimal, f the crediting periods per year, t the years and D the recurring deposit.
One implementation detail changes answers and is easy to miss: D is applied once per compounding period, not once per month. Set the frequency to Monthly when you enter a monthly deposit. Leave it on Annually and the same $100 becomes $100 per year, which collapses the deposit term by roughly a factor of twelve while the headline still says "Monthly Additional Deposit".
The effective annual rate reported alongside is (1 + r/f)^f - 1 — the APY a bank would have to advertise to match your nominal rate at that frequency.
Crediting frequency, priced
$10,000 at a nominal 8%, no deposits, ten years:
| Frequency | Effective annual rate | Ending balance |
|---|---|---|
| Annually | 8.000% | $21,589 |
| Semi-annually | 8.160% | $21,911 |
| Quarterly | 8.243% | $22,080 |
| Monthly | 8.300% | $22,196 |
| Daily | 8.328% | $22,253 |
The whole column spans $664. Between quarterly and daily — the range nearly every real account sits in — it spans $173. Raising the rate a single point to 9% monthly instead gives $24,514, more than three times the entire annual-to-daily spread. Frequency is a rounding detail. Rate and time are the story.
The default run, and the rule of 72 checked against it
$10,000, 8% nominal, monthly crediting, ten years, no deposits:
- Periodic rate
0.08 / 12 = 0.0066667over120periods (1.0066667)^120 = 2.21964- Final amount $22,196.40; interest earned $12,196.40; effective annual rate 8.30%; return on investment 122.0%
The rule of 72 predicts a double in 72 / 8 = 9 years. The exact answer at monthly compounding is ln(2) / ln(1.0066667) = 104.3 months, or 8.7 years — the shortcut runs about four months long. Its error grows with the rate: at 15% it predicts 4.8 years against an actual 4.6.
Now switch on a $250 monthly deposit on the same run. The deposit term contributes 250 x (2.21964 - 1) / 0.0066667 = $45,736, taking the balance to $67,933 against $40,000 of your own money in.
Reading the Effective Annual Rate and ROI lines
Four figures come back in Growth Projection mode: Final Amount, Total Interest Earned (final minus principal minus every deposit), Effective Annual Rate, and Return on Investment.
The last one needs a warning. ROI here is measured against the principal alone: (final - P) / P. With deposits switched on it inflates fast and stops meaning anything — on the $250-a-month run above it reads 579% while your actual money in was $40,000, not $10,000. When you are using deposits, read Total Interest Earned instead; if you want a single return figure for an investment that grew from one known value to another (rather than one you're projecting forward with a fixed rate), switch to the Return / CAGR tab.
The Effective Annual Rate line, by contrast, is the genuinely useful one: it converts whatever nominal rate and frequency you entered into a single number you can compare against a quoted APY.
Return / CAGR mode solves CAGR = (Ending Value / Starting Value)^(1/years) - 1. This is the correct way to describe a multi-year return as a single annual rate — and it is not the same thing as an "average annual return," which is just the arithmetic mean of each year's individual return and can overstate the real result whenever returns are volatile. A investment that goes up 50% then down 50% has an average annual return of 0% but a CAGR of about -13.4%, since $100 → $150 → $75 is a real loss.
What it answers well
Comparing two quoted offers at different crediting frequencies — type both in, read the effective annual rate line, and the comparison is settled in seconds. Sizing a lump sum you do not intend to touch: a 529 balance, an inheritance, a rung of a CD ladder. And showing time-sensitivity plainly: the same $10,000 at 8% monthly is $22,196 after ten years, $49,268 after twenty, and $109,359 after thirty. The gap between decades widens rather than repeating, which is the entire point of the exercise.
If you have a target rather than a projection, Savings Goal solves for the deposit instead. For a full working life with inflation applied, use Retirement.
What the ending balance is not
It is not purchasing power. At 2.5% inflation, the $22,196 above buys what $17,341 buys today. Every figure on this page is nominal.
It is not a portfolio. A fixed rate is exactly right for a CD and exactly wrong for an equity fund. The same average return delivered as a volatile sequence produces the same endpoint only if you never add or withdraw money along the way — and almost nobody does.
It is not net of tax or fees. Interest in a taxable account is ordinary income each year, which turns 8% gross into roughly 6.2% at a 22% marginal rate. Fund fees compound against you on the identical curve; the SEC's fee bulletin linked below works that example with real numbers.
Deposits are assumed level and never missed, and they land at the end of each period. Real contribution histories have gaps, and the gaps early in the term cost the most.
Frequently asked questions
Does compounding frequency actually matter?
Less than people assume. On $10,000 at 8% for ten years, moving from annual to daily crediting is worth $664, while moving the rate from 8% to 9% is worth $2,317. Compare rates first, frequency second.
My monthly deposit barely did anything. What went wrong?
Check the frequency selector. The deposit is applied once per compounding period, so with Annually selected your monthly figure is being contributed once a year. Set it to Monthly.
Why does the ROI line look absurd when I add deposits?
It divides the total gain by the starting principal only, ignoring every deposit. With deposits switched on, read Total Interest Earned instead — the Return/CAGR tab is built for a starting-and-ending-value comparison, not a series of contributions.
What's the difference between CAGR and average annual return?
Average annual return is the arithmetic mean of each year's percentage change; CAGR is the single compound rate that actually connects the starting and ending value. They diverge whenever returns are volatile — a 50% gain followed by a 50% loss averages to 0% but is a real loss, which CAGR correctly reflects as roughly -13.4% per year.
What is the rule of 72 and how wrong is it?
Divide 72 by the interest rate for an approximate doubling time. At 8% it says 9 years against an actual 8.7 at monthly compounding; the error grows with the rate, so treat it as a mental check rather than a calculation.
Is the Effective Annual Rate the same as APY?
Yes in substance. It is what your nominal rate compounds to over a year at the selected frequency, which is the figure US deposit accounts must advertise as APY.
Should I use a nominal or a real rate?
Either, but not both, and be consistent. Entering a nominal 8% gives a nominal balance; entering roughly 5.4% instead approximates the same result in today's purchasing power at 2.5% inflation.
Sources and further reading
Figures and definitions on this page are drawn from the following primary sources. If you find something out of date, tell us and we will correct it.