Multiple choice

John and Dave invested the same amount of money at 10% rate of interest for 2 years. John invested money compounded annually. Dave invested money compounded half yearly. The interest received by Dave after 2 years is what percent more than that received by John?

  1. 2.62%

  2. 3.12%

  3. 8.12%

  4. 12.02%

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

John: 10% compounded annually for 2 years = (1.1)^2 - 1 = 21%. Dave: 10% compounded half-yearly for 2 years (4 periods at 5%) = (1.05)^4 - 1 = 21.550625%. Difference = 21.550625 - 21 = 0.550625%. The question asks for percent more, which is (0.550625/21) * 100 = 2.622%.

AI explanation

Assuming a principal of 100, John's compound interest for two years at 10 percent is 100 x [(1.1)^2 minus 1], equalling 21. Dave's interest compounded half-yearly involves four periods at 5 percent each, calculated as 100 x [(1.05)^4 minus 1], which is approximately 21.5506. Dave's interest is [(21.5506 minus 21) / 21] x 100, equalling 2.62 percent more than John's interest.

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