IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Allowing for inflation
A price index rises by 4% in the first year, 6% in the second year and 5% in the third year. What is the equivalent constant annual rate of inflation over the three years?
The equivalent constant annual inflation rate is about 4.99%. Multiply the yearly factors 1.04, 1.06 and 1.05 to get 1.15752, then take the cube root. The arithmetic average of 5% overstates it because inflation compounds geometrically.
- A5.00%
- B4.99%Correct
- C5.01%
- D5.15%
- 15.70%
Explanation
Cumulative factor = 1.04 x 1.06 x 1.05 = 1.157520. Cube root: 1.157520^(1/3) = 1.0499 approx (1.0499^3 = 1.15730; 1.04992^3 = 1.15742... close to 1.15752 at 1.04995). So rate = 4.99% to two decimals when rounded as 4.99%. The simple average 5.00% ignores compounding. 15.70% is the total, not annual.
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