A sum becomes its double in $10$ years. Find the annual rate of simple interest.

### Concept & Sum Multipliers When a sum becomes "$n$" times itself, the simple interest earned is equal to $(n-1)$ times the original principal. $$ R = \frac{(n - 1) \times 100}{T} $$ ### Step-by-Step Solution - Let the principal sum be $P$. - The sum doubles, so the Amount ($A$) = $2P$. - Simple Interest ($SI$) = Amount - Principal = $2P - P = P$. - Time ($T$) = $10$ years. - Using the standard SI formula: - $SI = \frac{P \times R \times T}{100}$ - $P = \frac{P \times R \times 10}{100}$ - $1 = \frac{R \times 10}{100}$ - $1 = \frac{R}{10}$ - $R = 10\%$ ### Exam Strategy & Shortcut If money doubles, it means the interest earned is exactly $100\%$ of the principal. To find the rate, simply divide this $100\%$ by the number of years: $\frac{100}{10} = 10\%$. ### Common Pitfall A common error is to set the interest equal to $2P$ instead of the amount being $2P$, leading to double the actual interest rate. ### Final Answer Therefore, the correct answer is **10%**.