IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Duration, convexity and immunisation
A single payment of Rs 50,000 is due in exactly 7 years, and the valuation rate is 8% per annum effective. What is the discounted mean term (Macaulay duration) of this cashflow, in years?
The discounted mean term is 7.00 years. With a single payment, the PV-weighted average time is just the payment date, and the interest rate does not affect it. Dividing by 1.08 gives modified duration, not Macaulay duration.
- A7.56
- B6.48
- C3.50
- D7.00Correct
- 5.60
Explanation
The discounted mean term is the PV-weighted average of payment times. With one payment the weight is 1 at t = 7, so the DMT is 7.00 whatever the interest rate. The figure 6.48 is 7/1.08, which is the modified duration, not the Macaulay duration.
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