How many years will it take for an investment to treble at an annual interest rate of 10%?

The formula for simple interest is $A = P(1 + rt)$, where:

• $A$ is the final amount
• $P$ is the principal amount (initial investment)
• $r$ is the annual interest rate (as a decimal)
• $t$ is the time in years

From the problem:

• The money needs to treble, so $A = 3P$.
• The interest rate is $10\%$ per annum, so $r = 0.10$.

Divide both sides by $P$:

$$3 = 1 + 0.10t$$

Subtract 1 from both sides:

$$2 = 0.10t$$

Divide by 0.10:

$$t = \frac{2}{0.10}$$ $$t = 20$$

It will take 20 years for the amount of money to treble.

The final answer is $20 \text{ years}$.