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

The force of interest is a constant 8% per annum. What is the equivalent nominal rate of discount convertible quarterly, d(4), to two decimal places?

d(4) is 7.92%. Equating the quarterly discount accumulation to e to the power 0.08 gives d(4) = 4(1 - e^-0.02) = 0.0792. Nominal discount rates always lie below the force of interest, whereas nominal interest rates lie above it.

  1. A7.92%Correct
  2. B8.00%
  3. C8.08%
  4. D7.84%
  5. 8.16%

Explanation

Use (1 - d(4)/4)^-4 = e^0.08, so d(4) = 4(1 - e^-0.02). e^-0.02 = 0.980199, so d(4) = 4 x 0.019801 = 0.079203, i.e. 7.92%. The 8.08% option is the nominal interest rate i(4), which exceeds delta.

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