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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Annuity and accumulation functions

Rs 5,000 is invested for 3 years. The effective annual interest rates in years 1, 2 and 3 are 5%, 6% and 7% respectively. What is the accumulated value at the end of year 3?

The accumulated value is Rs 5,954.55. Each year's balance grows by that year's own rate, so the factor is 1.05 × 1.06 × 1.07 = 1.19091, and 5,000 times this gives the result. Using an average 6% rate for all three years gives a slightly different figure.

  1. ARs 5,788.13
  2. BRs 5,900.00
  3. CRs 5,955.08
  4. DRs 6,125.22
  5. Rs 5,954.55Correct

Explanation

Multiply the yearly accumulation factors: 1.05×1.06×1.07 = 1.19091. Then 5,000×1.19091 = 5,954.55. Using the average rate of 6% for all years gives 5,955.08, which is slightly different because rates compound rather than average.

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