What is a compound growth factor?

It is (1 + r)^n: what one unit grows to after n periods at rate r per period. Multiply your starting amount by the factor to get the future value. Example: 1.07^20 = 3.8697, so $10,000 at 7% for 20 years becomes about $38,697.

How long does money take to double at 7%?

Exactly ln 2 / ln 1.07 = 10.24 years. The Rule of 72 approximation gives 72 / 7 = 10.3 years, which is why it is such a popular shortcut.

What is 1.07 to the power of 20?

1.07^20 = 3.8697 (to four decimal places). At 7% annual growth, any starting amount grows about 3.87 times in 20 years.

Compound Growth Table — (1 + r)ⁿ Factors from 1% to 15%

How to use this table: find your growth rate, pick your number of years, and multiply your starting amount by the factor shown. Example: $10,000 at 7% for 20 years → factor 3.8697 → about $38,697. Every factor is (1 + r)ⁿ — the same exponent our future value calculator computes exactly, for any rate and any number of years.

Rate	Doubles in	5 yrs	10 yrs	15 yrs	20 yrs	25 yrs	30 yrs	40 yrs	50 yrs
1% (×1.01ⁿ)	69.7 yrs	1.0510	1.1046	1.1610	1.2202	1.2824	1.3478	1.4889	1.6446
2% (×1.02ⁿ)	35.0 yrs	1.1041	1.2190	1.3459	1.4859	1.6406	1.8114	2.2080	2.6916
2.5% (×1.025ⁿ)	28.1 yrs	1.1314	1.2801	1.4483	1.6386	1.8539	2.0976	2.6851	3.4371
3% (×1.03ⁿ)	23.4 yrs	1.1593	1.3439	1.5580	1.8061	2.0938	2.4273	3.2620	4.3839
3.5% (×1.035ⁿ)	20.1 yrs	1.1877	1.4106	1.6753	1.9898	2.3632	2.8068	3.9593	5.5849
4% (×1.04ⁿ)	17.7 yrs	1.2167	1.4802	1.8009	2.1911	2.6658	3.2434	4.8010	7.1067
4.5% (×1.045ⁿ)	15.7 yrs	1.2462	1.5530	1.9353	2.4117	3.0054	3.7453	5.8164	9.0326
5% (×1.05ⁿ)	14.2 yrs	1.2763	1.6289	2.0789	2.6533	3.3864	4.3219	7.0400	11.4674
6% (×1.06ⁿ)	11.9 yrs	1.3382	1.7908	2.3966	3.2071	4.2919	5.7435	10.2857	18.4202
7% (×1.07ⁿ)	10.2 yrs	1.4026	1.9672	2.7590	3.8697	5.4274	7.6123	14.9745	29.4570
7.5% (×1.075ⁿ)	9.6 yrs	1.4356	2.0610	2.9589	4.2479	6.0983	8.7550	18.0442	37.1897
8% (×1.08ⁿ)	9.0 yrs	1.4693	2.1589	3.1722	4.6610	6.8485	10.0627	21.7245	46.9016
9% (×1.09ⁿ)	8.0 yrs	1.5386	2.3674	3.6425	5.6044	8.6231	13.2677	31.4094	74.3575
10% (×1.1ⁿ)	7.3 yrs	1.6105	2.5937	4.1772	6.7275	10.8347	17.4494	45.2593	117.3909
12% (×1.12ⁿ)	6.1 yrs	1.7623	3.1058	5.4736	9.6463	17.0001	29.9599	93.0510	289.0022
15% (×1.15ⁿ)	5.0 yrs	2.0114	4.0456	8.1371	16.3665	32.9190	66.2118	267.8635	1,083.6574

Factors rounded to 4 decimal places; annual compounding. “Doubles in” is the exact doubling time ln 2 / ln(1 + r) — the Rule of 72 (72 ÷ rate) is the quick approximation.

Three things this table makes obvious

Small rate differences compound into huge outcome differences. Over 30 years, 5% turns $1 into $4.32 while 7% turns it into $7.61 — two percentage points nearly doubles the result. Time is the heavier lever. At 7%, going from 10 years (1.97×) to 40 years (14.97×) multiplies the payoff far more than any realistic rate improvement. And doubling times stack: at 7.2% money doubles roughly every 10 years, so 40 years is four doublings — 2×2×2×2 = 16×, which is why the 40-year factor at 7% sits near 15.

For a specific rate that isn’t in the table — say 1.024¹² or 1.1025²⁰ — the exponent calculator gives the exact value instantly, and the future value calculator turns it into dollars with a year-by-year breakdown. The formulas behind it are on the exponent cheat sheet.

Did you know?

The lily pond riddle. A lily patch doubles daily and covers the pond on day 30. When was it half covered? Day 29 — exponential growth does most of its work at the very end.
1% better every day. Improving 1% daily for a year compounds to 1.01³⁶⁵ ≈ 37.8× better. Getting 1% worse daily shrinks you to 0.03× — the gap between the two is over a thousandfold.
The last doubling wins. At 7%, your final 10 years earn more than the first 30 combined — the 40-year factor is 14.97, and more than half of it arrives in the last decade.
It works against you too. A credit card at 24% APR compounding daily doubles the debt in under 3 years if left unpaid — the same math as saving, pointed the other way.
Why 72 and not 69.3? The mathematically exact doubling constant is 100 · ln 2 ≈ 69.3, but 72 won because it divides cleanly by 2, 3, 4, 6, 8, 9, and 12 — mental math beat precision.
Ten doublings = a thousandfold. Every 10 doublings multiplies money by 2¹⁰ = 1,024, so doubling ten times turns $1,000 into over $1 million.
The quote Einstein never said. “Compound interest is the eighth wonder of the world” is attributed to Einstein everywhere — but there’s no evidence he ever said it. The math is wondrous enough without him.
Seven doublings per lifetime. At 7% money doubles roughly every decade, so a sum invested at birth doubles about seven times by age 70 — a 128× multiplier.

Compound Growth Table

Three things this table makes obvious

Sources & Further Reading