The compound interest accrued in two years on a principal amount of ₹15,800 is ₹7716.72 What is the rate of interest p.c.p.a?

Options

A. 0.22
B. 0.16
C. 0.18
D. Cannot be determined

Explanation

To find the rate of interest per annum (p.c.p.a) based on the given compound interest accrued over two years, we can follow these steps:

### Step 1: Identify the given values
- Principal Amount (P) = ₹15,800
- Compound Interest (CI) = ₹7,716.72
- Time (T) = 2 years

### Step 2: Calculate the Total Amount (A)
The total amount after 2 years can be calculated using the formula:
\[ A = P + CI \]
Substituting the values:
\[ A = 15,800 + 7,716.72 = 23,516.72 \]

### Step 3: Use the Compound Interest Formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^T \]
Where:
- A = Total amount after time T
- P = Principal amount
- r = Rate of interest
- T = Time in years

Substituting the known values:
\[ 23,516.72 = 15,800 \left(1 + \frac{r}{100}\right)^2 \]

### Step 4: Rearrange the equation to isolate the interest rate
First, divide both sides by the principal amount (15,800):
\[ \frac{23,516.72}{15,800} = \left(1 + \frac{r}{100}\right)^2 \]

Calculating the left side:
\[ 1.4844 = \left(1 + \frac{r}{100}\right)^2 \]

### Step 5: Take the square root of both sides
Taking the square root:
\[ \sqrt{1.4844} = 1 + \frac{r}{100} \]
Calculating the square root:
\[ 1.22 = 1 + \frac{r}{100} \]

### Step 6: Solve for r
Subtract 1 from both sides:
\[ 1.22 - 1 = \frac{r}{100} \]
\[ 0.22 = \frac{r}{100} \]

Now, multiply both sides by 100 to find the rate:
\[ r = 0.22 \times 100 = 22 \]

### Conclusion
The rate of interest per annum is **22%**.

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