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

Concept: In simple interest, the interest earned is directly proportional to time. If a certain sum doubles in a given time, then the interest earned in that time equals the principal.
Simple Interest formula: \[ SI = \frac{P \times R \times T}{100} \] Also, \[ \text{Amount} = P + SI \]
Step 1:Finding the interest earned in 5 years.
If the sum doubles in 5 years, then: \[ \text{Amount} = 2P \] Thus, \[ SI = 2P - P = P \] So, in 5 years the interest earned is equal to the principal.
Step 2:Finding the interest required to make the amount four times.
If the money becomes four times: \[ \text{Amount} = 4P \] Thus, required interest: \[ SI = 4P - P = 3P \]
Step 3:Using proportionality of simple interest with time.
If interest \(= P\) in \(5\) years, Then interest \(= 3P\) in: \[ 3 \times 5 = 15 \text{ years} \] Therefore, the money will become four times in 15 years.