At what rate per cent per annum will Rs 6,000 amount to Rs 6,615 in 2 years when interest is compounded annually ?

Answer

To find the rate per cent per annum at which Rs 6,000 will amount to Rs 6,615 in 2 years when interest is compounded annually, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 6,000
- Amount (A) = Rs 6,615
- Time (T) = 2 years

### Step 2: Use the compound interest formula
The formula for compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^t \]
Where:
- A = Amount after time t
- P = Principal amount
- r = Rate of interest per annum
- t = Time in years

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 6615 = 6000 \left(1 + \frac{r}{100}\right)^2 \]

### Step 4: Divide both sides by the principal (6000)
\[ \frac{6615}{6000} = \left(1 + \frac{r}{100}\right)^2 \]

### Step 5: Calculate the left side
Calculating the left side:
\[ \frac{6615}{6000} = 1.1025 \]
So we have:
\[ 1.1025 = \left(1 + \frac{r}{100}\right)^2 \]

### Step 6: Take the square root of both sides
Taking the square root gives:
\[ \sqrt{1.1025} = 1 + \frac{r}{100} \]

### Step 7: Calculate the square root
Calculating the square root:
\[ 1.05 = 1 + \frac{r}{100} \]

### Step 8: Solve for r
Subtracting 1 from both sides:
\[ \frac{r}{100} = 1.05 - 1 \]
\[ \frac{r}{100} = 0.05 \]

### Step 9: Multiply by 100 to find r
Multiplying both sides by 100:
\[ r = 0.05 \times 100 \]
\[ r = 5 \]

### Conclusion
The rate of interest per annum is **5%**.

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