IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Duration, convexity and immunisation
A 3-year annuity-certain pays Rs 100 at the end of each year. Using an effective annual interest rate of 10%, what is the discounted mean term of its payments?
The discounted mean term is 1.94 years. The present values of the three payments at 10% are 90.91, 82.64 and 75.13; weighting the times 1, 2 and 3 by these and dividing by the total of 248.69 gives about 1.94, below the undiscounted average of 2.
- A1.80 years
- B1.94 yearsCorrect
- C2.00 years
- D2.13 years
- 1.76 years
Explanation
PVs: 90.909, 82.645, 75.131; total 248.685. Time-weighted sum = 90.909 + 165.289 + 225.394 = 481.592. DMT = 481.592/248.685 = 1.94. The 2.00 option is the simple average of payment times, ignoring discounting.
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