IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value
A lender quotes a nominal rate of discount of 8% per annum convertible quarterly. What is the equivalent effective annual rate of interest, to two decimal places?
The effective annual interest rate is 8.42%. An 8% nominal discount rate convertible quarterly means a 2% discount per quarter, so the annual discount factor is 0.98 to the power 4, about 0.9224. Inverting gives 1.0842, so i is 8.42%. Treating 2% as interest would give 8.24%, which is wrong.
- A8.00%
- B8.24%
- C8.42%Correct
- D8.16%
- 8.67%
Explanation
The quarterly discount rate is 2%, so the quarterly discount factor is 0.98. Over a year v = 0.98^4 = 0.922368, so 1 + i = 1/0.922368 = 1.084166 and i = 8.42%. The 8.24% option wrongly treats 2% as a quarterly interest rate, giving 1.02^4 - 1.
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