Multiple choice

A bank offers 10% per annum interest. A customer deposits Rs. 3,600 each on 1st January and 1st July of a year. At the end of the year, the Compound interest earned is. (Compound Interest is calculated semi-annually)

  1. Rs. 549

  2. Rs. 2,232

  3. Rs. 558

  4. Rs. 279
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A Correct answer
Explanation

The first deposit of 3600 earns interest for 12 months (2 periods at 5% per period). The second deposit of 3600 earns interest for 6 months (1 period at 5%). Interest on first: 3600 * (1.05^2 - 1) = 3600 * 0.1025 = 369. Interest on second: 3600 * 0.05 = 180. Total interest = 369 + 180 = 549.

AI explanation

Since interest is compounded semi-annually, the half-yearly rate is 10% / 2 = 5%. The first deposit of Rs. 3600 earns interest for two half-year periods, growing to 3600 * (1.05)^2 = 3600 * 1.1025 = Rs. 3969. The second deposit of Rs. 3600 earns interest for one half-year period, growing to 3600 * 1.05 = Rs. 3780. The total maturity value is 3969 + 3780 = Rs. 7749; subtracting the total principal of 7200 yields a compound interest of Rs. 549.

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