An amount fetched a total simple interest of Rs. 3200 at the rate of 6.25% per year in 4 years. What is the amount (in Rs)?

Options

A. 13800
B. 11800
C. 12800
D. 14800

Answer

To find the total amount based on the simple interest earned, we can follow these steps:

### Step 1: Understand the Simple Interest Formula
The formula for calculating Simple Interest (SI) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (the initial amount of money)
- \( R \) = Rate of interest per year
- \( T \) = Time in years

### Step 2: Identify the Given Values
From the question, we have:
- Simple Interest (\( SI \)) = Rs. 3200
- Rate of Interest (\( R \)) = 6.25%
- Time (\( T \)) = 4 years

### Step 3: Substitute the Values into the Formula
We need to find the Principal amount (\( P \)). Rearranging the formula to solve for \( P \):
\[ P = \frac{SI \times 100}{R \times T} \]

Now substituting the values we have:
\[ P = \frac{3200 \times 100}{6.25 \times 4} \]

### Step 4: Calculate the Denominator
First, calculate \( R \times T \):
\[ R \times T = 6.25 \times 4 = 25 \]

### Step 5: Substitute Back into the Formula
Now substitute back into the formula for \( P \):
\[ P = \frac{3200 \times 100}{25} \]

### Step 6: Perform the Calculation
Now, calculate \( P \):
\[ P = \frac{320000}{25} = 12800 \]

### Step 7: Find the Total Amount
The total amount (A) is given by:
\[ A = P + SI \]
Substituting the values:
\[ A = 12800 + 3200 = 16000 \]

### Final Answer
The total amount is Rs. 16000.

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