The difference between C. I. (Compound interest) and S.I.(Simple interest) on a sum of Rs 4,000 for 2 years at 5% p.a. payable yearly is

Options

A. Rs 20
B. Rs 10
C. Rs 50
D. Rs 60

Answer

To find the difference between Compound Interest (C.I.) and Simple Interest (S.I.) on a sum of Rs 4,000 for 2 years at an interest rate of 5% per annum, we can follow these steps:

### Step 1: Calculate Simple Interest (S.I.)
The formula for Simple Interest is:
\[ S.I. = \frac{P \times R \times T}{100} \]
where:
- \( P = 4000 \) (Principal amount)
- \( R = 5 \) (Rate of interest)
- \( T = 2 \) (Time in years)

Substituting the values:
\[ S.I. = \frac{4000 \times 5 \times 2}{100} \]
\[ S.I. = \frac{40000}{100} = 400 \]

### Step 2: Calculate Compound Interest (C.I.)
The formula for Compound Interest is:
\[ C.I. = P \left(1 + \frac{R}{100}\right)^T - P \]

Substituting the values:
\[ C.I. = 4000 \left(1 + \frac{5}{100}\right)^2 - 4000 \]
\[ C.I. = 4000 \left(1 + 0.05\right)^2 - 4000 \]
\[ C.I. = 4000 \left(1.05\right)^2 - 4000 \]
Calculating \( (1.05)^2 \):
\[ (1.05)^2 = 1.1025 \]
Now substituting back:
\[ C.I. = 4000 \times 1.1025 - 4000 \]
\[ C.I. = 4410 - 4000 = 410 \]

### Step 3: Calculate the Difference between C.I. and S.I.
Now, we find the difference:
\[ \text{Difference} = C.I. - S.I. \]
\[ \text{Difference} = 410 - 400 = 10 \]

### Final Answer
The difference between Compound Interest and Simple Interest is Rs 10.

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