Find the principal which will amount to Rs. 4,000 in 4 years at 6.25% per annum.

Answer

To find the principal that will amount to Rs. 4,000 in 4 years at an interest rate of 6.25% per annum, we will follow these steps:

### Step 1: Write down the given information
- Amount (A) = Rs. 4,000
- Time (T) = 4 years
- Rate of Interest (R) = 6.25% per annum

### Step 2: Use the formula for Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal
- \(R\) = Rate of interest
- \(T\) = Time in years

### Step 3: Substitute the values into the SI formula
Substituting the known values into the formula:
\[ SI = \frac{P \times 6.25 \times 4}{100} \]

### Step 4: Simplify the expression for SI
First, convert 6.25% to a fraction:
\[ 6.25 = \frac{625}{100} \]
Now, substituting this back into the equation:
\[ SI = \frac{P \times \frac{625}{100} \times 4}{100} \]
This simplifies to:
\[ SI = \frac{P \times 625 \times 4}{10000} \]
\[ SI = \frac{2500P}{10000} \]
\[ SI = \frac{P}{4} \]

### Step 5: Use the formula for Amount (A)
The formula for the amount is:
\[ A = P + SI \]
Substituting the values we have:
\[ 4000 = P + \frac{P}{4} \]

### Step 6: Combine the terms
To combine the terms on the right side, convert \(P\) into a fraction:
\[ 4000 = \frac{4P}{4} + \frac{P}{4} \]
\[ 4000 = \frac{5P}{4} \]

### Step 7: Solve for Principal (P)
To isolate \(P\), multiply both sides by 4:
\[ 4000 \times 4 = 5P \]
\[ 16000 = 5P \]
Now, divide both sides by 5:
\[ P = \frac{16000}{5} \]
\[ P = 3200 \]

### Final Answer
The principal amount is Rs. 3200.

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