IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions
A nominal rate of discount of 8% per annum convertible quarterly is quoted. What is the equivalent effective annual rate of interest, to two decimal places?
The equivalent effective annual interest rate is 8.42%. A quarterly discount rate of 2% gives an annual discount factor of 0.98 to the fourth power, 0.922368. Taking the reciprocal gives an accumulation factor of 1.08417 per year.
- A8.24%
- B8.16%
- C8.42%Correct
- D7.76%
- 8.00%
Explanation
Quarterly discount rate is 0.02, so annual v = 0.98^4 = 0.922368. Then 1+i = 1/0.922368 = 1.08417, so i = 8.42%. 8.24% wrongly treats it as an interest rate of 2% per quarter. 7.76% is the effective annual discount rate, not the interest rate.
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