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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 [This Question was asked as TITA]

Updated On: Jan 15, 2026
  • 15000
  • 17000
  • 16000
  • 18000
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The Correct Option is C

Solution and Explanation

Provided information:

  • Final Amount \( A = 18522 \)
  • Interest Rate \( r = 10\% = 0.10 \)
  • Time Period \( t = 1.5 \) years
  • Compounding Frequency: Half-Yearly (\( n = 2 \))
  • Principal Amount \( P = ? \)

The formula for compound interest with half-yearly compounding is:

\[ A = P \left(1 + \frac{r}{n} \right)^{nt} \]

Substituting the given values:

\[ 18522 = P \left(1 + \frac{0.10}{2} \right)^{2 \times 1.5} \] \[ 18522 = P (1.05)^3 \] \[ 18522 = P \times 1.157625 \]

Calculating the Principal (\( P \)):

\[ P = \frac{18522}{1.157625} \approx 16000 \]

Result: The principal amount initially invested was: \[ \boxed{16000} \]

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