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

Payments of Rs 1,000 at time 1 and Rs 2,000 at time 3 (in years) are to be replaced by a single payment at time 2. At 5% effective per annum, what must this single payment be for the two arrangements to have equal value?

The single payment at time 2 must be Rs 2,954.76. The Rs 1,000 paid one year earlier is accumulated for one year at 5%, while the Rs 2,000 paid one year later is discounted for one year, and the results are added.

  1. ARs 3,000.00
  2. BRs 2,680.06
  3. CRs 3,052.38
  4. DRs 3,102.50
  5. Rs 2,954.76Correct

Explanation

Value at time 2 = 1,000 × 1.05 + 2,000 / 1.05 = 1,050.00 + 1,904.76 = 2,954.76. Rs 2,680.06 is the value at time 0, not time 2. Rs 3,052.38 moves the time-3 payment in the wrong direction, accumulating it instead of discounting it.

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