Multiple choice

The effective annual rate of interest corresponding to a nominal rate of 19% per annum payable half-yearly is:

  1. 38%

  2. 19.9%

  3. 39.81%

  4. 19%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When interest is compounded half-yearly, the nominal annual rate of 19% is halved to 9.5% per six-month period. The effective annual rate is calculated as (1 + 0.095)^2 - 1, which equals 19.9025%. Rounding this value to one decimal place gives 19.9%.

AI explanation

The effective annual rate for a nominal rate of 19 percent payable half-yearly is found using the formula Effective Rate = ((1 plus R / 200)^2 minus 1) * 100. Substituting the rate gives ((1 plus 0.095)^2 minus 1) * 100, which equals (1.095^2 minus 1) * 100. Calculating the square gives (1.199025 minus 1) * 100, resulting in an effective annual rate of 19.9 percent.

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