A sum of 400 amounts to 441 in 2 yr. What will be its amount, if the rate of interest is increased by 5% ?

Options

A. Rs 484
B. Rs 560
C. Rs 512
D. Rs600

Answer

To solve the problem step by step, we need to determine the amount after increasing the rate of interest by 5%.

### Step 1: Identify the given values
- Principal (P) = 400
- Amount (A) after 2 years = 441
- Time (T) = 2 years

### Step 2: Calculate the interest earned in 2 years
Interest (I) can be calculated using the formula:
\[ I = A - P \]
Substituting the values:
\[ I = 441 - 400 = 41 \]

### Step 3: Calculate the rate of interest for the original amount
The formula for compound interest is:
\[ A = P(1 + r)^T \]
Where \( r \) is the rate of interest per year. We can rearrange this to find \( r \):
\[ 441 = 400(1 + r)^2 \]
Dividing both sides by 400:
\[ \frac{441}{400} = (1 + r)^2 \]
Calculating the left side:
\[ 1.1025 = (1 + r)^2 \]
Taking the square root of both sides:
\[ 1 + r = \sqrt{1.1025} \]
Calculating the square root:
\[ 1 + r \approx 1.05 \]
Thus,
\[ r \approx 1.05 - 1 = 0.05 \text{ or } 5\% \]

### Step 4: Increase the rate of interest by 5%
New rate of interest:
\[ r_{new} = 5\% + 5\% = 10\% \]

### Step 5: Calculate the new amount after 2 years at the new interest rate
Using the compound interest formula again:
\[ A_{new} = P(1 + r_{new})^T \]
Substituting the values:
\[ A_{new} = 400(1 + 0.10)^2 \]
Calculating:
\[ A_{new} = 400(1.10)^2 \]
\[ A_{new} = 400 \times 1.21 \]
\[ A_{new} = 484 \]

### Final Answer
The amount after increasing the rate of interest by 5% will be **Rs. 484**.

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