It's easy to think "growing 5% a month means 60% more after a year." It doesn't. Compounded, it's about 79.6%. That gap is the power of compounding, and it's the heart of growth forecasting.
Simple vs. compound
Simple growth adds the same amount each period, always based on the starting value. From 100, adding 10 a month gives 220 after a year.
Compound growth applies each period's growth to the accumulated total so far. From 100 growing 10% a month, the second month adds 10% of 110, the third adds 10% of 121. Growth stacks on growth.
Final value = Initial × (1 + rate/100) ^ periods
The longer the horizon and the higher the rate, the more dramatically simple and compound growth diverge. That's why compounding is emphasized so heavily in long-term investing and business growth.
"Compound growth" and "future value" are the same calculation
The two phrases differ only in context; the formula is identical.
- Compound growth: an initial 10,000 growing 8% a year for 10 years is worth how much?
- Future value: this month's 5,000 users growing 6% a month become how many in a year?
Both are solved by initial × (1 + rate/100)^periods. Put a principal in the initial-value field and you get a compound final value; put a current business metric there and it becomes a future projection (a growth scenario).
Small differences, big outcomes
With compounding, small changes in rate and time change the result a lot. Starting from 10,000:
- 7% a year, 10 years → about 19,672
- 10% a year, 10 years → about 25,937
- 10% a year, 20 years → about 67,275
A 3-point difference, or an extra 10 years, multiplies the final value. So when building growth scenarios, it helps to enter optimistic, base, and conservative rates and view the range of outcomes together.
Things to watch
- It assumes a constant rate every period. If real growth varies, split the horizon into segments and calculate each.
- A negative rate models compound decline, shrinking by a fixed percentage each period: useful for churn-driven user decline or depreciation.
- Match the period unit to the rate. A monthly rate needs periods in months.
CAGR: past growth as a single number
If the calculation above looks forward, sometimes you instead want to summarize what average annual rate already-realized growth came out to. That's CAGR (Compound Annual Growth Rate). It needs only a start value, end value, and number of periods, and it's the standard way to fairly compare the long-run growth of different investments or businesses.
To try the numbers, use the Compound Growth Calculator for future value and the CAGR Calculator for a past annual rate. For a single-period change, the Growth Rate Calculator is the quickest.