How is the current cumulative rate level calculated from rate changes r_i?

• A. Sum of rate changes
• B. Product of (1 + r_i) over all rate changes
• C. Average of rate changes
• D. Maximum rate change

Answer: (B)

The current cumulative rate level is found by applying each rate change multiplicatively. Each change r_i scales the current level by a factor of (1 + r_i), so after all changes the level is the base level times the product of all those factors: ∏ (1 + r_i). This captures compounding, because each change affects subsequent levels.

For example, if the first change is 10% and the second is -5%, the level becomes original × 1.10 × 0.95 = original × 1.045, a 4.5% overall increase. Adding the changes would give 10% + (-5%) = 5%, which ignores compounding and is incorrect. Averaging or taking the maximum similarly misses the cumulative effect.