Question

A sum of money doubles itself in 5 years at simple interest. In how many years will it become four times itself?

• A. \(10\) years
• B. \(12\) years
• C. \(15\) years
• D. \(20\) years

Hint:

In simple interest, if a sum doubles in \(T\) years, it becomes four times in \(3T\) years because the interest must increase from \(P\) to \(3P\).

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This problem deals with simple interest. We are given the time it takes for an initial sum of money (Principal) to double, and we need to find the time it will take for the same sum to become four times its original value at the same interest rate.
Step 2: Key Formula or Approach:
The key concept is that in simple interest, the interest earned each year is constant.
Amount = Principal (P) + Simple Interest (SI).
Let the Principal be \(P\).
Step 3: Detailed Explanation:
Case 1: The sum doubles in 5 years.
When the sum doubles, the Amount becomes \(2P\).
The Simple Interest (SI) earned is:
\[ SI_1 = \text{Amount} - \text{Principal} = 2P - P = P \] So, an interest equal to the principal (\(P\)) is earned in 5 years.
Case 2: The sum becomes four times itself.
When the sum becomes four times, the Amount becomes \(4P\).
The total Simple Interest (SI) that needs to be earned is:
\[ SI_2 = \text{Amount} - \text{Principal} = 4P - P = 3P \] We need to find the time it takes to earn an interest of \(3P\).
Since the interest earned per year is constant (Simple Interest), we can use a direct proportion:
If an interest of \(P\) is earned in 5 years,
Then an interest of \(3P\) will be earned in \(3 \times 5 = 15\) years.
Step 4: Final Answer:
The sum of money will become four times itself in 15 years.