One of the most appealing ways to grow money is compound interest. It is the idea that "interest earns interest." So at what interest rate, and after how many years, does your principal double? Today I will sort this question out very simply.
β The basic formula for doubling your principal (compound interest)
First, the mathematically exact formula.
T = ln(2) / ln(1 + r)
- T: the time it takes to double (in years)
- r: the annual interest rate (for 5%, enter 0.05)
For example, at 5% compound interest a year:
T = ln(2) / ln(1 + 0.05) β 14.2 years
In other words, it takes a little over 14 years.
β Too hard? That's why there is the "Rule of 72"
In real investing, people don't calculate the formula above every time. Instead, a very handy approximation called the Rule of 72 is widely used.
T β 72 / r(%)
For example:
- 6% a year β
72 / 6 = 12 years - 9% a year β
72 / 9 = 8 years
The rule is especially accurate when the interest rate is around 6β10%.
β Doubling time by interest rate (Rule of 72)
| Annual interest rate | Time to double |
|---|---|
| 3% | 24 years |
| 5% | 14.4 years |
| 7% | 10.3 years |
| 10% | 7.2 years |
| 12% | 6 years |
| 18% | 4 years |
β Besides 72, there are rules of 69, 70 and 75?
- Rule of 69
- The more mathematically exact value is 69.3 (derived from the logarithm).
- Rule of 70
- An easy, intuitive version to calculate (also often used in finance)
- Rule of 75
- Sometimes used as a slightly conservative version when accounting for after-tax returns or inflation
β Applying it to real investments
Now let's look at how it applies in real life with a few cases.
π Case β Stable long-term investing
- Investment: a US S&P 500 index fund
- Historical average annual return: about 8% (before tax)
- Applied:
T β 72 / 8 = 9 years - What it means:
if you keep an 8% return over the long term, your principal doubles about every 9 years.
For example, if you invested 30 million won,
β about 60 million won after 9 years
β about 120 million won after 18 years
β about 240 million won after 27 years!
π That's how powerful compounding is.
π Case β‘ A savings bank deposit
- Interest rate: a high-interest savings account at 4% a year
- Applied:
T β 72 / 4 = 18 years - What it means:
doubling your principal with bank interest takes 18 years or more.
π Case β’ Dividend growth stocks
- Return: 10% a year, combining dividends and share price gains
- Applied:
T β 72 / 10 = 7.2 years - What it means:
your assets double every seven years or so.
This is why people who invest steadily in dividend stocks for more than ten years build wealth.
π Case β£ Real estate (a conservative scenario)
- Average annual return (including rent and capital gains): about 5%
- Applied:
T β 72 / 5 = 14.4 years - What it means:
your principal doubles after about 14 to 15 years.
β Just remember this!
- Compound interest β the magic of getting rich
- If the formula feels too complicated, memorize the Rule of 72
- The higher the rate, the more explosive the compounding
- The longer the time, the more powerful compounding becomes
β Appendix: calculating it in Excel
If you want to calculate it yourself, enter this in Excel:
=LN(2)/LN(1 + interest_rate)Example: for a 5% interest rate β =LN(2)/LN(1+0.05) β about 14.2
β A final word
If you want to become rich, don't obsess over returns. Understand compounding and make time your friend.