Radhika invested an amount of Rs. 6000 for 2 years. At what rate of compound interest will she get compound interest of Rs. 615 at the end of two year ?

Options

A. 3 p.c.p.a
B. 4 p.c.p.a
C. 6 p.c.p.a
D. 5 p.c.p.a

Answer

To find the rate of compound interest at which Radhika will earn a compound interest of Rs. 615 after 2 years on an investment of Rs. 6000, we can follow these steps:

### Step 1: Calculate the Total Amount
First, we need to calculate the total amount after 2 years, which is the principal plus the compound interest.

\[ \text{Total Amount} = \text{Principal} + \text{Compound Interest} = 6000 + 615 = 6615 \]

### Step 2: Use the Compound Interest Formula
The formula for the amount \( A \) in compound interest is:

\[ A = P \left(1 + \frac{r}{100}\right)^n \]

Where:
- \( A \) = Total Amount
- \( P \) = Principal
- \( r \) = Rate of interest
- \( n \) = Number of years

Substituting the known values into the formula:

\[ 6615 = 6000 \left(1 + \frac{r}{100}\right)^2 \]

### Step 3: Simplify the Equation
To isolate the term with \( r \), we divide both sides by 6000:

\[ \frac{6615}{6000} = \left(1 + \frac{r}{100}\right)^2 \]

Calculating the left side:

\[ \frac{6615}{6000} = 1.1025 \]

So, we have:

\[ 1.1025 = \left(1 + \frac{r}{100}\right)^2 \]

### Step 4: Take the Square Root
Next, we take the square root of both sides to solve for \( 1 + \frac{r}{100} \):

\[ \sqrt{1.1025} = 1 + \frac{r}{100} \]

Calculating the square root:

\[ 1 + \frac{r}{100} = 1.05 \]

### Step 5: Solve for \( r \)
Now, we can isolate \( r \):

\[ \frac{r}{100} = 1.05 - 1 = 0.05 \]

Multiplying both sides by 100 gives us:

\[ r = 0.05 \times 100 = 5 \]

### Conclusion
Thus, the rate of compound interest \( r \) is:

\[ \boxed{5\%} \]

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