At what percentage rate, compound interest compounded annually for a sum of Rs 40,000, will amount to Rs 44,100 in two years ?

Options

A. 2
B. 7.5
C. 5
D. 4

Answer

To find the percentage rate at which the compound interest compounded annually for a sum of Rs 40,000 will amount to Rs 44,100 in two years, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = Rs 40,000
- Amount (A) = Rs 44,100
- Time (n) = 2 years

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

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 44,100 = 40,000 \left(1 + \frac{r}{100}\right)^2 \]

### Step 4: Divide both sides by the principal
To isolate the compound interest factor, divide both sides by 40,000:
\[ \frac{44,100}{40,000} = \left(1 + \frac{r}{100}\right)^2 \]

### Step 5: Simplify the left side
Calculating the left side:
\[ 1.1025 = \left(1 + \frac{r}{100}\right)^2 \]

### Step 6: Take the square root of both sides
To solve for \(1 + \frac{r}{100}\), take the square root of both sides:
\[ \sqrt{1.1025} = 1 + \frac{r}{100} \]
Calculating the square root:
\[ 1.05 = 1 + \frac{r}{100} \]

### Step 7: Isolate the rate (r)
Subtract 1 from both sides:
\[ 0.05 = \frac{r}{100} \]

### Step 8: Multiply by 100 to find r
To find the rate, multiply both sides by 100:
\[ r = 0.05 \times 100 \]
\[ r = 5 \]

### Conclusion
The percentage rate at which the compound interest compounded annually for the sum of Rs 40,000 will amount to Rs 44,100 in two years is **5%**.

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