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

An annuity-immediate pays Rs 10,000 per year for 10 years. At 6% effective annual interest, which expression gives its present value?

The present value of an annuity-immediate is the payment times (1 - v^n)/i, here 10,000 x (1 - 1.06^-10)/0.06. Using d in the denominator gives the annuity-due, and (1.06^10 - 1)/0.06 gives the accumulated value.

  1. A10,000 x (1.06^10 - 1)/0.06
  2. B10,000 x (1 - 1.06^-10)/0.06Correct
  3. C10,000 x (1 - 1.06^-10)/(0.06/1.06)
  4. D10,000 x 1.06^-10
  5. 10,000 x 10 x 1.06^-5

Explanation

An annuity-immediate has payments at year ends, so PV = P x a(10) = P(1 - v^10)/i. Option 0 is the accumulated value. Option 2 uses the discount rate d, which gives the annuity-due.

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