An amount fetched a total simple interset 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 when given the simple interest, we can use the formula for simple interest and the relationship between principal, interest, and total amount.

**Step 1: Understand the formula for Simple Interest (SI)**

The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount
- \( R \) = Rate of interest per year
- \( T \) = Time in years

**Step 2: Identify the given values**

From the question, we have:
- \( SI = 3200 \) Rs
- \( R = 6.25\% \)
- \( T = 4 \) years

**Step 3: Calculate the Principal (P)**

We can rearrange the formula to find the principal:
\[ P = \frac{SI \times 100}{R \times T} \]

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

**Step 4: Calculate the denominator**

First, calculate \( 6.25 \times 4 \):
\[ 6.25 \times 4 = 25 \]

**Step 5: Substitute back into the formula**

Now substitute this value back into the equation for \( P \):
\[ P = \frac{3200 \times 100}{25} \]

**Step 6: Perform the multiplication and division**

Calculate \( 3200 \times 100 = 320000 \).

Now divide by 25:
\[ P = \frac{320000}{25} = 12800 \]

**Step 7: Calculate the Total Amount (A)**

The total amount \( A \) can be calculated using:
\[ A = P + SI \]
Substituting the values we found:
\[ A = 12800 + 3200 = 16000 \]

Thus, the total amount is:
\[ A = 16000 \text{ Rs} \]

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

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