What is the difference between the maturity value of two deposits of Rs.5,000 each invested for 2 years (i) at 5% simple interest and (ii) at the same interest compounded annually?
A. Rs. 11.00
B. Rs. 11.50
C. Rs. 12.00
D. Rs. 12.50

Options

A. A
B. C
C. B
D. D

Answer

To solve the problem, we need to find the difference between the maturity values of two deposits of Rs. 5,000 each, invested for 2 years at a rate of 5%: one using simple interest (SI) and the other using compound interest (CI).

### Step-by-Step Solution

**Step 1: Calculate the maturity value using Simple Interest (SI)**

The formula for calculating the maturity value using simple interest is:

\[ \text{Maturity Value (SI)} = P + \left( \frac{P \times r \times t}{100} \right) \]

Where:
- \( P = 5000 \) (Principal)
- \( r = 5 \) (Rate of interest)
- \( t = 2 \) (Time in years)

Calculating the interest:

\[ \text{Interest} = \frac{5000 \times 5 \times 2}{100} = \frac{50000}{100} = 500 \]

Now, adding the interest to the principal:

\[ \text{Maturity Value (SI)} = 5000 + 500 = 5500 \]

**Step 2: Calculate the maturity value using Compound Interest (CI)**

The formula for calculating the maturity value using compound interest is:

\[ \text{Maturity Value (CI)} = P \left(1 + \frac{r}{100}\right)^t \]

Substituting the values:

\[ \text{Maturity Value (CI)} = 5000 \left(1 + \frac{5}{100}\right)^2 = 5000 \left(1 + 0.05\right)^2 = 5000 \left(1.05\right)^2 \]

Calculating \( (1.05)^2 \):

\[ (1.05)^2 = 1.1025 \]

Now, calculating the maturity value:

\[ \text{Maturity Value (CI)} = 5000 \times 1.1025 = 5512.50 \]

**Step 3: Find the difference between the two maturity values**

Now, we find the difference between the maturity values calculated:

\[ \text{Difference} = \text{Maturity Value (CI)} - \text{Maturity Value (SI)} = 5512.50 - 5500 = 12.50 \]

### Final Answer

The difference between the maturity values is **Rs. 12.50**.