Select the correct answerA sum of money (P) doubles in 10 years. In how many years it will be triples at the same rate of simple interest?Options30152010

1. Break Down the Problem

To find out how long it will take for a sum of money $P$ to triple at the same rate of simple interest, we need to:

1. Determine the rate of interest using the information that $P$ doubles in 10 years.
2. Use the rate to calculate the time required for $P$ to triple.

2. Relevant Concepts

Using the formula for simple interest: $A = P + SI \\ SI = P \cdot r \cdot t$ where $A$ is the final amount, $P$ is the principal, $r$ is the rate of interest, and $t$ is the time in years.

3. Analysis and Detail

1. Doubling in 10 years: $2P = P + P \cdot r \cdot 10 \\ SI = P \cdot r \cdot 10 = P \\ r \cdot 10 = 1 \\ r = \frac{1}{10} = 0.1 \text{ or } 10\%$

2. Tripling the principal: To triple the principal: $3P = P + P \cdot r \cdot t \\ 3P - P = P \cdot r \cdot t \\ 2P = P \cdot r \cdot t \\ 2 = r \cdot t \\ t = \frac{2}{r} = \frac{2}{0.1} = 20 \text{ years}$

4. Verify and Summarize

The calculation shows that at an interest rate of $10\%$, it takes 20 years for a sum of money to triple.

Final Answer

It will take 20 years for the sum of money to triple at the same rate of simple interest. Therefore, the correct answer is 20.