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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Interest rates over different time periods

An effective annual rate of interest is 9%. Find the equivalent nominal rate of interest per annum convertible monthly, to two decimal places.

The equivalent nominal rate convertible monthly is 8.65%. Solve 12 times the quantity 1.09 to the power one-twelfth minus one. The monthly rate is about 0.7207%, and multiplying by twelve gives roughly 8.65% per annum.

  1. A8.65%
  2. B8.74%Correct
  3. C8.29%
  4. D9.00%
  5. 8.57%

Explanation

i(12) = 12[(1.09)^(1/12) - 1]. ln1.09 = 0.0861777; divided by 12 = 0.0071815; exp = 1.0072074; minus 1 = 0.0072074; times 12 = 8.649%, i.e. 8.65%. Check: 1.0072074^12 = 1.09. The 8.74% option is wrongly 9% divided by 12 compounded... actually it is not equivalent, and 9.00% ignores conversion.

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