if money doubles in 10 years at compound interest, the approximate annual rate is:

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^n$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate, and $n$ is the number of years. Given that $A = 2P$ and $n = 10$. Substitute into the formula: $2P=P(1 + r)^{10}$.

Step2: Simplify the equation

Divide both sides of the equation $2P = P(1 + r)^{10}$ by $P$ (assuming $P\neq0$). We get $2=(1 + r)^{10}$.

Step3: Solve for $r$

Take the 10 - th root of both sides: $1 + r=2^{\frac{1}{10}}$. Then $r = 2^{\frac{1}{10}}-1$. Calculate $2^{\frac{1}{10}}\approx1.07177$. So $r\approx0.07177$ or $7.18%$.

Answer:

Approximately $7.18%$