What sum will amount to Rs. 6600 in 4 years at `8%` p.a. simple interest ?

Options

A. Rs. 6000
B. Rs. 5000
C. Rs. 6200
D. None of these

Answer

To find the sum (principal amount) that will amount to Rs. 6600 in 4 years at an interest rate of 8% per annum using simple interest, we can follow these steps:

### Step 1: Understand the formula for Amount in Simple Interest
The formula for the amount (A) in simple interest is:
\[ A = P + SI \]
Where:
- \( A \) = Amount
- \( P \) = Principal (sum)
- \( SI \) = Simple Interest

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

### Step 3: Substitute the known values
From the question:
- Amount \( A = 6600 \)
- Rate \( R = 8\% \)
- Time \( T = 4 \) years

Now, substituting these values into the Simple Interest formula:
\[ SI = \frac{P \times 8 \times 4}{100} \]
\[ SI = \frac{32P}{100} \]

### Step 4: Substitute SI back into the Amount formula
Now, substitute the expression for Simple Interest back into the Amount formula:
\[ 6600 = P + \frac{32P}{100} \]

### Step 5: Combine like terms
To combine the terms, we can express \( P \) as \( \frac{100P}{100} \):
\[ 6600 = \frac{100P + 32P}{100} \]
\[ 6600 = \frac{132P}{100} \]

### Step 6: Solve for P
To isolate \( P \), multiply both sides by 100:
\[ 6600 \times 100 = 132P \]
\[ 660000 = 132P \]

Now, divide both sides by 132:
\[ P = \frac{660000}{132} \]
\[ P = 5000 \]

### Conclusion
The principal amount (sum) that will amount to Rs. 6600 in 4 years at 8% per annum simple interest is Rs. 5000.

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