Question

If a certain sum invested under compounded interest becomes 4 times of itself in 15 years then in how many years wil the same sum become 16 times of itself?

• A. 30 years
• B. 45 years
• C. 60 years
• D. 64 years

Answer 1

The Correct Option is A

Finding the Time Required for the Amount to Become 16 Times

Step 1: Define the Compound Interest Formula

The compound interest formula is: 

\[ A = P \left(1 + \frac{r}{100} \right)^t \]

Step 2: Given Condition for Quadrupling

The amount quadruples in 15 years, so:

\[ 4P = P \left(1 + \frac{r}{100} \right)^{15} \]

Dividing both sides by \( P \):

\[ 4 = \left(1 + \frac{r}{100} \right)^{15} \]

Step 3: Condition for 16 Times

We need to find the time \( t \) when the amount becomes 16 times, i.e.:

\[ 16P = P \left(1 + \frac{r}{100} \right)^t \]

Dividing both sides by \( P \):

\[ 16 = \left(1 + \frac{r}{100} \right)^t \]

Step 4: Relating the Two Equations

Since we know that \( 16 = 4^2 \), we can rewrite it as:

\[ \left(1 + \frac{r}{100} \right)^t = \left( \left(1 + \frac{r}{100} \right)^{15} \right)^2 \]

Thus, equating the exponents:

\[ t = 2 \times 15 = 30 \text{ years} \]

Final Answer:

Thus, the correct answer is 30 years (Option A).