Step 1: Understanding the Concept:
Simple Interest (SI) is calculated solely on the original principal amount for the duration of the loan or investment.
The "Amount" (A) mentioned in such problems refers to the total accumulated value at the end of the period, which is the sum of the Principal (P) and the Interest (SI) earned.
Step 2: Key Formula or Approach:
1. \( \text{Simple Interest (SI)} = \frac{P \times R \times T}{100} \)
2. \( \text{Total Amount (A)} = P + SI = P + \frac{P \times R \times T}{100} = P \left(1 + \frac{RT}{100}\right) \)
Step 3: Detailed Explanation:
Given values from the question:
Accumulated Amount (A) = Rs. 9680
Rate of interest (R) = 10% per annum
Time duration (T) = 4 years
Let's plug these values into the Amount formula:
\[ 9680 = P \left(1 + \frac{10 \times 4}{100}\right) \]
\[ 9680 = P \left(1 + \frac{40}{100}\right) \]
\[ 9680 = P (1 + 0.40) \]
\[ 9680 = 1.4P \]
To isolate the Principal (P), we divide the total amount by 1.4:
\[ P = \frac{9680}{1.4} \]
Multiply both numerator and denominator by 10 to clear the decimal:
\[ P = \frac{96800}{14} \]
Now, performing the division by 14:
\[ 96 \div 14 = 6 \text{ (since } 14 \times 6 = 84\text{), remainder 12} \]
\[ 128 \div 14 = 9 \text{ (since } 14 \times 9 = 126\text{), remainder 2} \]
\[ 20 \div 14 = 1 \text{ (since } 14 \times 1 = 14\text{), remainder 6} \]
\[ 60 \div 14 = 4 \text{ (since } 14 \times 4 = 56\text{), remainder 4} \]
\[ 40 \div 14 \approx 28... \]
\[ P \approx 6914.28 \]
Step 4: Final Answer:
The principal amount is Rs. 6914.28.