Multiple choice

How much more does a man get by investing 40000 at 40% p.a. compound interest, compounded half yearly, than at 40% p.a. compound interest, compounded yearly per one year?

  1. 1000

  2. 1200

  3. 1500

  4. 1600
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Principal = 40000, Rate = 40%. Yearly: A = 40000 * (1 + 0.4) = 56000. Interest = 16000. Half-yearly: Rate = 20%, Time = 2 periods. A = 40000 * (1 + 0.2)^2 = 40000 * 1.44 = 57600. Interest = 17600. Difference = 17600 - 16000 = 1600.

AI explanation

When compounded annually, the amount is 40000 multiplied by (1.40) = 56000. When compounded half-yearly, the rate becomes 20% per half-year for two periods, making the amount 40000 multiplied by (1.20) squared = 40000 multiplied by 1.44 = 57600. The difference between the two amounts is 57600 - 56000 = 1600.

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