How Long to Double Money at 3%
At 3% a year, money doubles in 23.4 years. The Rule of 72 says 24.0.
Doubles in
23.4 years
Quadruples in
46.9 years
Grows 8 times in
70.3 years
Rule of 72 estimate
24.0 years
What different amounts become
| Start | After 23.4 years | After 46.9 years | After 70.3 years |
|---|---|---|---|
| $1,000 | $2,000 | $4,000 | $8,000 |
| $5,000 | $10,000 | $20,000 | $40,000 |
| $10,000 | $20,000 | $40,000 | $80,000 |
| $25,000 | $50,000 | $100,000 | $200,000 |
| $50,000 | $100,000 | $200,000 | $400,000 |
| $100,000 | $200,000 | $400,000 | $800,000 |
Growth over time at 3%
| Years | $1,000 becomes | $10,000 becomes | Growth |
|---|---|---|---|
| 5 | $1,159 | $11,593 | 1.16x |
| 10 | $1,344 | $13,439 | 1.34x |
| 15 | $1,558 | $15,580 | 1.56x |
| 20 | $1,806 | $18,061 | 1.81x |
| 25 | $2,094 | $20,938 | 2.09x |
| 30 | $2,427 | $24,273 | 2.43x |
| 40 | $3,262 | $32,620 | 3.26x |
| 50 | $4,384 | $43,839 | 4.38x |
How it is worked out
Years to double = ln(2) / ln(1 + r)
ln = natural logarithm, r = rate as a decimal.
The Rule of 72 is the shortcut version. Divide 72 by the rate.
At 3% the shortcut is off by 0.6 years.