Multiple choice

Find the amount which Ram will get on Rs. 4096, if he gave it for 18 months at $12\frac{1}{2}$% per annum,interest being compounded half yearly.

  1. $Rs. 4913$
  2. $Rs. 4425$
  3. $Rs. 4814$
  4. $Rs. 4124$
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A Correct answer
Explanation

Principal = 4096. Rate = 12.5% per annum = 6.25% per half-year. Time = 18 months = 3 half-years. Amount = 4096 * (1 + 6.25/100)^3 = 4096 * (1 + 1/16)^3 = 4096 * (17/16)^3 = 4096 * 4913 / 4096 = 4913.

AI explanation

The time period of 18 months equals 3 half-years, and the half-yearly rate is 12.5% / 2 = 6.25%, which is equivalent to 1/16. Using the compound amount formula, Amount = 4096 * (1 + 1/16)^3 = 4096 * (17/16)^3. Calculating this gives 4096 * 4913 / 4096, which results in Rs. 4913.

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