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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Present value and accumulated value of cashflow streams

A deferred annuity pays Rs 2,000 at the end of each year for years 4 to 10 inclusive (7 payments). At an effective annual rate of 5%, what is its present value at time 0?

The present value is Rs 9,996.97. Payments run from year 4 to year 10, so the value is 2,000 times the difference between the 10-year and 3-year annuity-immediate values, equivalently v cubed times a 7-year annuity. Deferring by four years or not at all gives wrong values.

  1. ARs 9,996.97Correct
  2. BRs 11,572.75
  3. CRs 9,520.93
  4. DRs 8,351.57
  5. Rs 10,496.82

Explanation

PV = 2,000(a10 - a3) = 2,000(7.721735 - 2.723248) = 2,000 × 4.998487 = 9,996.97. This equals 2,000 v^3 a7. Rs 11,572.75 is 2,000 a7 with no deferment. Rs 9,520.93 over-defers by one year (v^4 a7).

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