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

An account grows with a constant force of interest of 6% per annum. What is the effective annual rate of interest, to two decimal places?

The effective annual rate is 6.18%. With a constant force of interest δ = 0.06, the annual accumulation factor is e^0.06 = 1.061837, so i = e^δ − 1 = 6.18%. The figure 5.83% is the effective discount rate, which is a different quantity.

  1. A6.00%
  2. B6.09%
  3. C6.18%Correct
  4. D5.83%
  5. 6.27%

Explanation

With a constant force δ, the effective annual rate is i = e^δ − 1. So i = e^0.06 − 1 = 1.061837 − 1 = 6.18%. The 5.83% option comes from using 1 − e^(−0.06), which is the effective annual discount rate, not the interest rate. The 6.09% option comes from the monthly nominal rate i(12) at 6%.

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