Question

Difference between SI and CI for 2 year @ 10% is Rs. 150. Find the principal.

Hint:

Memorize the direct formulas for the difference between CI and SI for 2 years and 3 years to save time in exams. For 3 years, the formula is \(P(R/100)^2(3 + R/100)\).

Answer 1

Correct Answer: 15000

Step 1: Understanding the Question:
We are given the difference between Compound Interest (CI) and Simple Interest (SI) for a period of 2 years at a specific rate. We need to find the initial sum of money (Principal).
Step 2: Key Formula or Approach:
There is a direct formula for the difference between CI and SI for 2 years: \[ \text{Difference} = P \left( \frac{R}{100} \right)^2 \] where P is the Principal and R is the rate of interest per annum.
Step 3: Detailed Explanation:
We are given: - Difference = Rs. 150 - R = 10% - Time = 2 years Substitute the given values into the formula: \[ 150 = P \left( \frac{10}{100} \right)^2 \] \[ 150 = P \left( \frac{1}{10} \right)^2 \] \[ 150 = P \left( \frac{1}{100} \right) \] Now, solve for P: \[ P = 150 \times 100 \] \[ P = 15000 \] Step 4: Final Answer:
The principal is Rs. 15,000.