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

The nominal rate of discount convertible quarterly is d(4) = 8% per annum. Find the equivalent effective annual rate of interest, to two decimal places.

The equivalent effective annual interest rate is about 8.42%, which is closest to 8.43%. Quarterly discount is 2% per quarter, so the annual discount factor is 0.98 to the power 4, 0.92237. Inverting gives an accumulation factor of 1.0842.

  1. A8.24%
  2. B8.43%Correct
  3. C8.50%
  4. D8.16%
  5. 8.70%

Explanation

1 - d = (1 - d(4)/4)^4 = 0.98^4 = 0.92236816. So 1+i = 1/0.92236816 = 1.08417, giving i = 8.42%. Computing precisely: 1/0.92236816 = 1.084160, so i = 8.42%, nearest option is 8.43%. Option 8.24% is the interest-convertible equivalent (1.02^4 - 1 = 8.24%), which wrongly treats the rate as an interest rate.

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