emg3000

04-24-2011, 11:31 PM

This problem states that 2003 Average Written Premium is $933.33. It also states that there was a rate decrease of 20% implemented on July 1, 2003. Calculating on-level premium is central to the problem. The official exam answers state that the on-level average written premium is $840. Exposures are written uniformly throughout the year.

From the official exam answers:

CAY 2003 – Half of the written premium needs to be adjusted down by 20%. The adjusted CAY 2003 average written premium is

1⁄2(933.33) + 1⁄2(933.33)(0.8) = 840

Am I missing something? If the average written premium for the year was $933.33 but there was a rate change halfway through, does that not imply that half the exposures were written at a rate level greater than $933.33 and half written at some level below $933.33?

My calculation is as follows:

[(Rate)(0.5 Exposures)+(0.8 Rate)(0.5 Exposures)] /[Exposures] = 933.33

=> (0.9 Rate) = $933.33

=> Rate = $1037.03

=> On-level Rate = ($1037.03)(0.8) = $829.63

So, what's up with this?

From the official exam answers:

CAY 2003 – Half of the written premium needs to be adjusted down by 20%. The adjusted CAY 2003 average written premium is

1⁄2(933.33) + 1⁄2(933.33)(0.8) = 840

Am I missing something? If the average written premium for the year was $933.33 but there was a rate change halfway through, does that not imply that half the exposures were written at a rate level greater than $933.33 and half written at some level below $933.33?

My calculation is as follows:

[(Rate)(0.5 Exposures)+(0.8 Rate)(0.5 Exposures)] /[Exposures] = 933.33

=> (0.9 Rate) = $933.33

=> Rate = $1037.03

=> On-level Rate = ($1037.03)(0.8) = $829.63

So, what's up with this?