Multiple choice

What sum will become Rs 9826 in 18 months if the rate of interest is $2\, \displaystyle \frac{1}{2}$% per annum and the interest is compounded half-yearly?

  1. Rs. 9466.54

  2. Rs. 9646.54

  3. Rs. 9566.54

  4. Rs. 9456.54
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A Correct answer
Explanation

Rate = 2.5% p.a. compounded half-yearly = 1.25% per half-year. Time = 18 months = 3 half-years. Amount = P(1 + 1.25/100)^3 = 9826. P = 9826 / (1.0125)^3 = 9826 / 1.03797 = 9466.54.

AI explanation

Using the compound interest formula with a half-yearly rate, the rate becomes 1.25% for 3 periods over 18 months. The principal equals the final amount of 9826 divided by (1 + 1.25/100) cubed, or 9826 divided by (1.0125)^3. Calculating this gives 9826 divided by 1.037970703125, which results in an initial sum of Rs. 9466.54.

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