What is the difference (in Rs) between the compound interest (compounded annually) and simple interest for 3 years on a principal of Rs 2500 at the rate of 30% per annum is:
(a)742.5
(b)624.5
(c)714.5
(d)825.25

Options

A. 742.5
B. 624.5
C. 714.5
D. 825.25

Answer

To find the difference between the compound interest (CI) and simple interest (SI) for 3 years on a principal of Rs 2500 at the rate of 30% per annum, we can follow these steps:

### Step 1: Calculate Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( P = 2500 \) (Principal)
- \( R = 30 \) (Rate of interest)
- \( T = 3 \) (Time in years)

Substituting the values:
\[ SI = \frac{2500 \times 30 \times 3}{100} = \frac{2500 \times 90}{100} = 2250 \]

### Step 2: Calculate Compound Interest (CI)
The formula for Compound Interest is:
\[ CI = P \left(1 + \frac{R}{100}\right)^T - P \]
Substituting the values:
\[ CI = 2500 \left(1 + \frac{30}{100}\right)^3 - 2500 \]
\[ = 2500 \left(1.3\right)^3 - 2500 \]
Calculating \( (1.3)^3 \):
\[ (1.3)^3 = 1.3 \times 1.3 \times 1.3 = 2.197 \]
Now substituting back:
\[ CI = 2500 \times 2.197 - 2500 \]
\[ = 5492.5 - 2500 = 2992.5 \]

### Step 3: Calculate the Difference
Now, we find the difference between CI and SI:
\[ \text{Difference} = CI - SI = 2992.5 - 2250 = 742.5 \]

### Final Answer
The difference between the compound interest and simple interest for 3 years on a principal of Rs 2500 at the rate of 30% per annum is Rs 742.5.

### Options:
(a) 742.5
(b) 624.5
(c) 714.5
(d) 825.25

The correct answer is (a) 742.5.

---