Question:
A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is
A person invested a certain amount of money at 10% annual interest, compounded half-yearly. After one and a half years, the interest and principal together became Rs 18522. The amount, in rupees, that the person had invested is
Updated On: Jul 25, 2025
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Solution and Explanation
The annual interest rate is 10%, compounded semi-annually.
Hence, each half-yearly rate \( R = 5\% \), and the number of compounding periods is \( n = 3 \).
Let the original sum be \( P \).
According to the formula for compound interest:
\[ P \times \left(1 + \frac{10}{200}\right)^3 = 18522 \]
Solving for \( P \):
\[ P = 18522 \times \left(\frac{20}{21}\right)^3 \]
\[ P = 18522 \times \frac{8000}{9261} = 16000 \]
\[ \boxed{P = 16000} \]
Summary:
- Interest Rate (annual) = 10%
- Compounded every 6 months → 2 periods per year
- Rate per period = 5%
- Number of periods = 3
- Final Amount = 18522
- Principal = ₹16000
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