Multiple choice

Consider a bond which offers 10% p.a. rate of interest to be compounded half yearly. What is the effective rate of interest per annum?

  1. 10%

  2. 10.25%

  3. 5%

  4. 20%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Suppose Rs. 100 is invested. The rate per annum is 10%, i.e. 5% per half year. The amount after first half year will be 100 + 5%, i.e. Rs. 105 and amount after second half year, i.e. one year will be 105 + 5%, i.e. Rs. 110.25. Thus, effective rate of interest per annum is 110.25 - 100 = 10.25%.

AI explanation

With compounding, a nominal annual rate applied more than once per year yields an effective annual rate higher than the nominal rate. Compounding 10% per annum at 5% every six months gives an effective rate of (1 + 0.05)² − 1 = 1.1025 − 1 = 0.1025, or 10.25%. The effective rate is always at least as large as the nominal rate whenever compounding happens more than once a year, which rules out 10% or 5% as the answer.

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