A sum of Rs. 400/- amounts to Rs. 480/-in 4 years. What will it amount to if the rate of interest in increased 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 these instructions:

### 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 we have:
\[ \text{SI} = 480 - 400 = 80 \]

### Step 3: Use the Simple Interest formula to find the rate (R)
The formula for Simple Interest is also given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
We can rearrange this to find R:
\[ R = \frac{\text{SI} \times 100}{P \times T} \]
Substituting the known values:
\[ R = \frac{80 \times 100}{400 \times 4} \]
\[ R = \frac{8000}{1600} = 5\% \]

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

### Step 5: Calculate the new Simple Interest with the increased rate
Using the Simple Interest formula again:
\[ \text{SI}' = \frac{P \times R' \times T}{100} \]
Substituting the new rate:
\[ \text{SI}' = \frac{400 \times 7 \times 4}{100} \]
\[ \text{SI}' = \frac{11200}{100} = 112 \]

### Step 6: Calculate the new Amount (A')
The new amount will be:
\[ A' = P + \text{SI}' \]
Substituting the values:
\[ A' = 400 + 112 = 512 \]

### Final Answer
The amount will be Rs. 512 when the rate of interest is increased by 2%.

---