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1. कुनै सावाँको चक्रिय ब्याज वार्षिक 8% को दरले 2 वर्षमा रु. 312 हुन्छ भने त्यति अवधि र त्यही व्याजदरले उक्त सावाँको साधारण ब्याज निकाल्नुहोस् ।

(The compound interest on a certain sum for 2 years at 8% per annum compounded annually is Rs 312. Find the simple interest for the same time and at the same rate.)

[2065C]

Ans: Rs 300



Answer :

GinnyAnswer
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.

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