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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: Jan 15, 2026
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Solution and Explanation

The annual interest rate is 10%, compounded semi-annually. Consequently, the rate for each half-year is \( R = 5\% \), and there are \( n = 3 \) compounding periods.

Let the initial sum be denoted by \( P \).

Applying the compound interest formula:

\[ P \times \left(1 + \frac{10}{200}\right)^3 = 18522 \]

To find \( P \):

\[ P = 18522 \times \left(\frac{20}{21}\right)^3 \]

\[ P = 18522 \times \frac{8000}{9261} = 16000 \]

\[ \boxed{P = 16000} \]

Summary:

  • Annual Interest Rate = 10%
  • Compounding Frequency = Semi-annually (2 periods per year)
  • Interest Rate per Period = 5%
  • Total Number of Periods = 3
  • Final Amount = 18522
  • Principal Amount = ₹16000
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