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Question 20 : 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

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Explanatory Answer

A 10% annual interest is a 5% bi-annual interest.
Hence interst for half an year is 5%.

The Principal, P is invested for 1.5 years or 3 terms of half years.
Therefore, P (1 + 5%)3 = 18522
P(1.05)3 = 18522
P × \\frac{21}{20}) × \\frac{21}{20}) × \\frac{21}{20}) = 18522
P × \\frac{7}{20}) × \\frac{7}{20}) × \\frac{7}{20}) = 686
P × \\frac{1}{20}) × \\frac{1}{20}) × \\frac{1}{20}) = 2
P = 2 × 20 × 20 × 20 = 16000.

The answer is, "16000"

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