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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Time value of money: compound interest and discounting

An investment grows at 6% per annum compound effective. What constant annual simple interest rate would give the same accumulation over exactly 5 years?

The equivalent simple rate is 6.76% per annum. Compounding at 6% for 5 years gives a factor of 1.3382256, and spreading the 33.82% total growth evenly over 5 years under simple interest gives 0.3382256 ÷ 5 ≈ 6.76%.

  1. A6.00%
  2. B6.76%Correct
  3. C7.50%
  4. D5.64%
  5. 6.38%

Explanation

Compound factor = 1.06^5 = 1.3382256. Equate 1 + 5i = 1.3382256, so i = 0.3382256/5 = 0.067645, i.e. 6.76%. The 5.64% option divides by 6 instead of 5, and 6.00% ignores interest on interest.

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