Question

The difference between the compound interest compounded annually on a certain sum for 4 years at the rate of 7.5% per annum is Rs. 4800. Find the sum.

Hint:

For compound interest problems: \begin{itemize} \item Carefully note the rate and time, \item Use compound interest formulas accurately, \item Difference-based CI questions often use factor comparison. \end{itemize}

Answer 1

Step 1: Let the principal be \(P\).
Step 2: The rate of interest \(= 7.5% = \dfrac{15}{2}%\).
Step 3: Difference between compound interests for 4 years at this rate is given as Rs. 4800.
Step 4: Using the standard compound interest difference relation: \[ P\left[\left(1+\frac{7.5}{100}\right)^4 - \left(1+\frac{7.5}{100}\right)^3\right] = 4800 \]
Step 5: Solving the above equation, we get: \[ P = \text{Rs. } 1,35,211 \]
Step 6: Hence, the required sum is Rs. 1,35,211.