Multiple choice

A bank offers $5\%\ C.I.$ calculated on a half-yearly basis. A customer deposits $Rs.\ 1600$ each on 1st January and $1st$ July of a year. At the end of the year, the amount he would have gained by way of interest is

  1. $Rs.\ 120$
  2. $Rs.\ 121$
  3. $Rs.\ 122$
  4. $Rs.\ 123$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Half-yearly rate = 2.5%. First 1600 earns interest for 1 year (2 periods): 1600 * (1.025)^2 - 1600 = 1600 * 1.050625 - 1600 = 81. Second 1600 earns interest for 6 months (1 period): 1600 * 0.025 = 40. Total interest = 81 + 40 = 121.

AI explanation

The Rs 1600 deposited on January 1st earns 5% interest compounded over two half-yearly periods, giving interest of 1600(1.025)^2 - 1600 = 81. The Rs 1600 deposited on July 1st earns interest for only one half-year period, yielding 1600(0.025) = 40. The total interest is 81 + 40 = 121. The interest gained is Rs 121.

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