To find the simple interest given the compound interest and other parameters, we can follow a structured approach:
1. Identify Given Information:
- Compound Interest (CI) = Rs 312
- Annual Rate (R) = 8% or 0.08 when converted to decimal
- Time Period (T) = 2 years
2. Determine the Principal Amount (P):
- We use the compound interest formula to determine the principal amount:
[tex]\[
CI = P \left(1 + \frac{R}{100}\right)^T - P
\][/tex]
Rearranging to solve for \(P\):
[tex]\[
P = \frac{CI}{\left(1 + \frac{R}{100}\right)^T - 1}
\][/tex]
Substituting values:
[tex]\[
P = \frac{312}{\left(1 + 0.08\right)^2 - 1}
\][/tex]
Using the calculations, we find:
[tex]\[
P \approx 1874.9999999999989 \approx 1875 \, \text{(rounded to 2 decimal places)}
\][/tex]
3. Calculate Simple Interest (SI):
- The formula for Simple Interest is:
[tex]\[
SI = P \times R \times T
\][/tex]
Substituting the values:
[tex]\[
SI = 1875 \times 0.08 \times 2
\][/tex]
Performing the multiplication:
[tex]\[
SI \approx 299.99999999999983 \approx 300 \, \text{(rounded to 2 decimal places)}
\][/tex]
4. Conclusion:
- The simple interest for the given principal amount over the same time and at the same rate is approximately Rs 300.
Thus, the simple interest for 2 years at 8% per annum on the same principal amount is Rs 300.
