Multiple choice

An usurer claims to be lending money at simple interest. But, he includes the interest every six months for calculating the principal. If he is charging an interest of 15%, then the effective rate of interest becomes

  1. 15.56%

  2. 15%

  3. 16%

  4. 15.65%

  5. 15.75%
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A Correct answer
Explanation

The interest is compounded semi-annually. The effective rate is calculated as (1 + r/n)^n - 1, where r = 0.15 and n = 2. This gives (1 + 0.15/2)^2 - 1 = (1.075)^2 - 1 = 1.155625 - 1 = 0.155625, or 15.56%.

AI explanation

Since the interest is compounded every six months, the half-yearly rate is 15% / 2 = 7.5% or 0.075. For a year, the effective growth factor is (1 + 0.075)^2 = 1.155625. Subtracting 1 and converting to a percentage gives an effective rate of 15.5625%, which rounds to 15.56%.

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