Multiple choice

In what time will Rs 64000 amount to Rs 68921 at 5% per annum interest being compounded half-yearly?

  1. $\displaystyle 1\frac{1}{2}$ years
  2. $\displaystyle \frac{2}{3}$ years
  3. $2$ years

  4. None of these
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A Correct answer
Explanation

Amount = P(1 + r/200)^(2n). 68921/64000 = (1 + 5/200)^(2n) = (1.025)^(2n). 68921/64000 = (41/40)^3. So 2n = 3, n = 1.5 years.

AI explanation

Using the compound interest formula 64000(1 + 0.025)^n = 68921 for half-yearly compounding at 2.5% per period, we divide to get (1.025)^n = 1.076265625. Recognizing that 1.025 cubed equals 1.076265625, we find n = 3 half-yearly periods. Therefore, the time is 1 and a half years.

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