What would be the C.I. on rs. 17500 at the rate of 12% p.a. after 2 years?

Options

A. a. rs. 4442
B. b. rs. 4452
C. c. rs. 4462
D. d. rs. 4482

Answer

To find the Compound Interest (C.I.) on Rs. 17,500 at the rate of 12% per annum after 2 years, we can follow these steps:

### Step 1: Identify the formula for Compound Interest
The formula for Compound Interest (C.I.) is given by:
\[ C.I. = P \left(1 + \frac{r}{100}\right)^n - P \]
where:
- \( P \) = Principal amount
- \( r \) = Rate of interest per annum
- \( n \) = Time period in years

### Step 2: Substitute the values into the formula
Given:
- \( P = 17,500 \)
- \( r = 12 \)
- \( n = 2 \)

Substituting these values into the formula:
\[ C.I. = 17500 \left(1 + \frac{12}{100}\right)^2 - 17500 \]

### Step 3: Simplify the expression inside the brackets
Calculate \( 1 + \frac{12}{100} \):
\[ 1 + \frac{12}{100} = 1 + 0.12 = 1.12 \]

### Step 4: Raise the result to the power of 2
Now, we need to calculate \( (1.12)^2 \):
\[ (1.12)^2 = 1.2544 \]

### Step 5: Multiply by the principal amount
Now, multiply this result by the principal amount:
\[ C.I. = 17500 \times 1.2544 - 17500 \]
Calculating \( 17500 \times 1.2544 \):
\[ 17500 \times 1.2544 = 21949.2 \]

### Step 6: Subtract the principal from the result
Now, subtract the principal amount from this result:
\[ C.I. = 21949.2 - 17500 = 4449.2 \]

### Step 7: Round off to the nearest whole number
Since we typically deal with whole numbers in currency, we can round this off:
\[ C.I. \approx 4450 \]

### Final Answer
The Compound Interest on Rs. 17,500 at the rate of 12% per annum after 2 years is approximately Rs. 4450.

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