Multiple choice

What is the difference between compound interest on Rs. 5000 for 1½ years at 4% per annum if the interest is compounded yearly and half-yearly, respectively?

  1. Rs. 1.40

  2. Rs. 2.04

  3. Rs. 8.30

  4. Rs. 9.80

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Yearly compounding: 5000 * (1 + 0.04)^1 * (1 + 0.02) = 5000 * 1.04 * 1.02 = 5304. Half-yearly compounding: 5000 * (1 + 0.02)^3 = 5000 * 1.061208 = 5306.04. The difference is 5306.04 - 5304 = 2.04.

AI explanation

For yearly compounding, the amount is 5000 x (1 + 4/100) x (1 + 2/100), which equals 5000 x 1.04 x 1.02 to give Rs. 5304. For half-yearly compounding over three half-years, the amount is 5000 x (1 + 2/100)^3, which equals 5000 x 1.061208 to give Rs. 5306.04. The difference between the two amounts is 5306.04 minus 5304, which is Rs. 2.04.

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