A sum of Rs 400 amounts to Rs 480 in 4 years. What will it amount to If the rate of interset is increase by 2% ?

Options

A. Rs 484
B. Rs 560
C. Rs 512
D. None of these

Answer

To solve the problem step by step, we will follow the process of calculating the new amount after increasing the rate of interest by 2%.

### Step 1: Identify the given values
- Principal (P) = Rs 400
- Amount (A) after 4 years = Rs 480
- Time (T) = 4 years

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = \text{A} - \text{P} \]

Substituting the values:
\[ \text{SI} = 480 - 400 = Rs 80 \]

### Step 3: Calculate the rate of interest (R)
We know that:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Rearranging the formula to find R:
\[ R = \frac{\text{SI} \times 100}{P \times T} \]

Substituting the values:
\[ R = \frac{80 \times 100}{400 \times 4} \]
\[ R = \frac{8000}{1600} = 5\% \]

### Step 4: Increase the rate of interest by 2%
New Rate (R') = R + 2% = 5% + 2% = 7%

### Step 5: Calculate the new Simple Interest with the increased rate
Using the new rate:
\[ \text{SI'} = \frac{P \times R' \times T}{100} \]

Substituting the values:
\[ \text{SI'} = \frac{400 \times 7 \times 4}{100} \]
\[ \text{SI'} = \frac{11200}{100} = Rs 112 \]

### Step 6: Calculate the new amount (A')
Now, we can find the new amount:
\[ A' = P + \text{SI'} \]
\[ A' = 400 + 112 = Rs 512 \]

### Final Answer:
The new amount after increasing the rate of interest by 2% will be Rs 512.

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