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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Equation of value

An annuity pays Rs 1,000 at the end of year 1, Rs 2,000 at the end of year 2 and Rs 3,000 at the end of year 3. The effective annual interest rate is 10%. What is the present value?

The present value is Rs 4,815.93. Discount each payment at 10%: 1,000 for one year, 2,000 for two years and 3,000 for three years, and add the results. Using a level average payment or advance timing gives other values.

  1. ARs 481.59
  2. BRs 4,815.93Correct
  3. CRs 4,973.70
  4. DRs 5,297.52
  5. Rs 6,000.00

Explanation

PV = 1000(v + 2v² + 3v³) = 1000(0.909091 + 1.652893 + 2.253944) = Rs 4,815.93. Rs 4,973.70 replaces the payments by a level Rs 2,000 (the mean payment). Rs 5,297.52 is the value if each payment were one year earlier.

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