The Investment Growth Formula
Investment growth is measured with compound growth: a lump sum grows by FV = PV × (1 + r)n, and regular contributions add the annuity term PMT × [((1 + r)n − 1) / r]. Two numbers describe the result — total return (how much it grew overall) and annualized return, or CAGR (the steady yearly rate that produces that growth). This guide shows each formula, how to convert between total and annualized return, and what the growth multiple looks like across rates and timeframes.
The core growth formula
At its heart, investment growth uses the same compound formula as future value. A single invested amount grows to:
PV is what you invest today, r is the return per period as a decimal, and n is the number of periods. Each period the balance is multiplied by (1 + r), and because that multiplication repeats, growth compounds rather than adds. $10,000 invested at an assumed 7 percent for 20 years becomes about $38,700 — the same engine described in how compound interest works and derived step by step in the future value formula.
What makes "investment growth" its own topic is how you measure that result. Once money has grown, you usually want to express the gain in two standard ways: the total return and the annualized return.
Total return vs annualized return (CAGR)
Total return is the overall percentage gain from start to finish:
Annualized return, also called the compound annual growth rate (CAGR), is the single steady yearly rate that would turn the beginning value into the ending value:
They answer different questions. Total return tells you how much you made in total; CAGR tells you the equivalent smooth yearly pace, which is what lets you compare investments held for different lengths of time. The table follows $10,000 growing at a steady 7 percent.
| Years | Ending value | Total return | Annualized (CAGR) |
|---|---|---|---|
| 10 | $19,672 | +97% | 7% |
| 20 | $38,697 | +287% | 7% |
| 30 | $76,123 | +661% | 7% |
Notice the CAGR stays 7 percent while the total return balloons. That is the trap in headline numbers: a "+661% return" sounds extraordinary, but spread over 30 years it is the same 7 percent a year as the "+97%" earned over 10. Always check which one a source is quoting.
Growth with regular contributions
Most investing involves adding money over time, not a single deposit. For a stream of equal contributions, the growth formula gains the annuity term:
The first part grows your starting balance; the second grows every future contribution. You calculate them separately and add the results. One caution: when contributions are monthly, r and n must be monthly too (annual rate ÷ 12, and months for n). The full treatment, with tables by amount, lives in future value with monthly contributions, and you can run both parts together on the investment growth calculator.
The growth multiple
A quick way to picture compounding is the growth multiple — how many times your money multiplies, which is simply (1 + r)n. It is independent of the dollar amount, so it works for any starting sum.
| Annual return | 10 years | 20 years | 30 years |
|---|---|---|---|
| 5% | 1.6× | 2.7× | 4.3× |
| 7% | 2.0× | 3.9× | 7.6× |
| 10% | 2.6× | 6.7× | 17.4× |
The bottom-right corner shows why time and rate matter so much together: at 10 percent over 30 years money multiplies more than 17 times, versus roughly 4 times at 5 percent. For a fast mental estimate of doubling time, the Rule of 72 divides 72 by the rate — at 7 percent, money doubles about every 10 years, which is why the 30-year column lands near 7.6× (close to two and a half doublings).
Real vs nominal growth
Every figure so far is nominal — it ignores inflation. Real growth strips inflation out to show purchasing power, using an inflation-adjusted rate roughly equal to your return minus the inflation rate.
At an assumed 7 percent with about 3 percent inflation, the real growth rate is closer to 3.9 percent. So $10,000 growing to a nominal $76,000 over 30 years is worth around $31,000 in today's money — still triple your purchasing power, but a very different headline. Whenever a projection spans decades, decide whether you want the nominal number or the inflation-adjusted one before you act on it.
Assumptions behind the formula
- A constant rate. The formula applies one steady r. Real returns vary year to year; r is a long-run average, and CAGR is the smoothed equivalent of a bumpy path.
- Matching periods. r and n must share a time unit — annual with annual, monthly with monthly.
- Reinvested returns. Compounding assumes gains stay invested. Spending dividends or interest lowers the effective growth.
- Nominal by default. Results ignore inflation, taxes and fees unless you adjust for them.
A worked example
You invest $20,000 today and add $300 a month for 25 years at an assumed 7 percent. Work the two parts, then combine.
| Component | Formula | Future value at 7% (25y) |
|---|---|---|
| $20,000 lump sum | PV(1 + r)n | ~$114,500 |
| $300 / month | PMT × [((1 + r)n − 1) / r] | ~$243,000 |
| Combined | sum of the two | ~$357,500 |
You contributed $110,000 in total ($20,000 plus $300 × 300 months), so over $247,000 of the result is growth. Expressed as CAGR on the whole cash-flow stream the rate is still 7 percent — the formula and the metric describe the same outcome from two angles. Try your own figures on the investment growth calculator.
Frequently asked questions
The bottom line
Investment growth runs on the compound formula — FV = PV(1 + r)n for a lump sum, plus the annuity term for contributions — and is summarised by two numbers: total return and annualized return (CAGR). Total return is the headline gain; CAGR is the steady yearly pace that makes different investments comparable. The growth multiple, (1 + r)n, is a quick way to feel the combined power of rate and time, and adjusting for inflation turns a nominal projection into real purchasing power.
To put numbers to your own plan, open the investment growth calculator or the future value calculator, and browse the Learn hub for the ideas behind them.
Disclaimer: This guide is for general educational purposes only and is not financial advice. The examples use assumed rates of return to illustrate how investments compound; they are projections, not guarantees, and actual results vary with markets, inflation, taxes and fees. Consider speaking with a qualified financial professional before making decisions about your own money.