The difference between compound interest (compounded annually) and simple interest on a certain sum of money at the rate of 20 per cent per annum (rate of-Interest is same for simple and compound interest) for two years is 60. If the same sum is invested in scheme ABC which offers simple interest at the rate of 15 per cent per annum what will be the interest earned on this particular scheme after 4 years?

Options

A. rs 650
B. rs 900
C. rs 1200
D. rs 1500

Answer

To solve the problem step by step, we will first find the principal amount (P) using the information given about the difference between compound interest and simple interest for 2 years. Then we will calculate the interest earned from scheme ABC after 4 years.

### Step 1: Understand the difference between Compound Interest and Simple Interest
The difference between compound interest (CI) and simple interest (SI) for 2 years can be calculated using the formula:
\[ \text{Difference} = \frac{P \times r^2}{100^2} \]
where \( P \) is the principal amount, and \( r \) is the rate of interest.

### Step 2: Set up the equation
Given that the difference is 60 and the rate \( r \) is 20% per annum, we can set up the equation:
\[ 60 = \frac{P \times 20^2}{100^2} \]

### Step 3: Simplify the equation
Substituting \( 20^2 = 400 \) and \( 100^2 = 10000 \):
\[ 60 = \frac{P \times 400}{10000} \]

### Step 4: Solve for P
Rearranging the equation to solve for \( P \):
\[ P = \frac{60 \times 10000}{400} \]
\[ P = \frac{600000}{400} \]
\[ P = 1500 \]

### Step 5: Calculate the Simple Interest for Scheme ABC
Now, we need to calculate the interest earned on the same principal amount \( P = 1500 \) at the rate of 15% per annum for 4 years using the simple interest formula:
\[ \text{SI} = \frac{P \times r \times t}{100} \]
where \( r = 15\% \) and \( t = 4 \) years.

### Step 6: Substitute the values into the formula
Substituting the values:
\[ \text{SI} = \frac{1500 \times 15 \times 4}{100} \]

### Step 7: Calculate the Simple Interest
Calculating the above expression:
\[ \text{SI} = \frac{1500 \times 60}{100} \]
\[ \text{SI} = \frac{90000}{100} \]
\[ \text{SI} = 900 \]

### Final Answer
The interest earned on scheme ABC after 4 years is **900**.

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