IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Duration, convexity and immunisation
A level annuity-immediate pays Rs 1 at the end of each of the next 3 years. At an effective annual interest rate of 10%, what is its discounted mean term (Macaulay duration) in years, to two decimal places?
The discounted mean term is 1.94 years. Present values are 0.9091, 0.8264 and 0.7513, summing to 2.4869. The time-weighted sum is 4.8159, and dividing gives 1.94. This is below 2 because earlier payments carry more present value.
- A2.00
- B1.76
- C2.19
- D1.94Correct
- 1.84
Explanation
PVs: 0.909091, 0.826446, 0.751315; total a3 = 2.486852. Weighted sum = 0.909091 + 1.652893 + 2.253944 = 4.815928. DMT = 4.815928/2.486852 = 1.94. The value 2.00 is the unweighted mean of 1, 2, 3, ignoring discounting.
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