You Double Your Money in Five Years. Here’s Why Your Return Isn’t 20% Per Year

Many investors assume that if their money doubles in five years, they must have earned a 20% return each year. This assumption ignores compounding, which plays a crucial role in investment growth. Misunderstanding this can lead to unrealistic expectations and poor financial decisions. To assess returns accurately, it’s essential to distinguish between simple and compound interest, as well as nominal and annualized rates.

Compound vs Simple Returns

Simple returns apply a fixed percentage to the original investment each year, without reinvesting gains. For example, at a 10% annual simple return, a $10,000 investment grows by $1,000 each year, reaching $15,000 after five years.

Compounded returns, however, reinvest gains, calculating each year’s return on a growing balance. With a 10% annual compound return, the same $10,000 investment grows to approximately $16,105 in five years. Over longer periods, the impact of compounding becomes even more significant, making it a key factor in long-term growth.

Annualized vs Nominal Rates

Investment performance is often expressed in nominal or annualized terms. The nominal rate represents the total percentage increase over the entire period but does not account for time. This can be misleading, as a high nominal return over several years does not necessarily indicate strong annual growth.

The annualized rate, or compound annual growth rate (CAGR), provides a clearer measure by showing what the return would be if earned consistently each year. This allows for meaningful comparisons across investments of different durations. If an investment grows from $10,000 to $20,000 in five years, the nominal return is 100%, but the annualized return is lower due to compounding.

CAGR is calculated using the formula:

CAGR = (Ending Value / Beginning Value)^(1 / Years) – 1

Applying this:

CAGR = (20,000 / 10,000)^(1 / 5) – 1 = 0.1487 or 14.87%

This means the investment effectively grew at an average rate of 14.87% per year, not 20%, because each year’s return was applied to a growing balance.

Doubling Period Math

To estimate how long it takes for an investment to double, the Rule of 72 provides a quick approximation by dividing 72 by the annual return percentage. For a 10% return, the doubling period is roughly 7.2 years.

For a precise calculation, the formula is:

t = ln(2) / ln(1 + r)

where t is the number of years to double, r is the annual return rate (expressed as a decimal), and ln represents the natural logarithm.

Using a 14.87% annual return:

t = ln(2) / ln(1.1487) ≈ 5

This confirms that an investment compounding at this rate doubles in five years. Unlike the Rule of 72, this method provides exact results for any percentage.