Question:
Difference between SI and CI for 2 year @ 10% is Rs. 150. Find the principal.
Difference between SI and CI for 2 year @ 10% is Rs. 150. Find the principal.
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Think about the additional interest earned in the second year on the first-year interest. At $10\%$, this extra amount is $1\%$ of the principal.
Updated On: Aug 14, 2026
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Correct Answer: 15000
Approach Solution - 1
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.
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.
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Approach Solution -2
Concept:
Step 1: Express first-year interest.
At $10\%$, the first-year interest on principal $P$ is $0.1P$.
Step 2: Find the extra second-year interest under compounding.
The extra interest is $10\%$ of $0.1P$, which equals $0.01P$.
Step 3: Use the given difference.
$0.01P=150$, so $P=150/0.01=15000$.
Final Answer: Rs. $15{,}000$
- For two years, the extra compound interest is the interest earned in year two on the first-year interest.
- This gives the difference without memorising a separate formula.
Step 1: Express first-year interest.
At $10\%$, the first-year interest on principal $P$ is $0.1P$.
Step 2: Find the extra second-year interest under compounding.
The extra interest is $10\%$ of $0.1P$, which equals $0.01P$.
Step 3: Use the given difference.
$0.01P=150$, so $P=150/0.01=15000$.
Final Answer: Rs. $15{,}000$
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