Calculations Pertaining to Workers' Compensation Insurance Benefit Levels: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Basic Ratemaking, cited below. Students are encouraged to read these pages before attempting the problems. This study guide is entirely an independent effort by Mr. Stolyarov and is not affiliated with any organization(s) to whose textbooks it refers, nor does it represent such organization(s).

Some of the questions here ask for short written answers based on the reading. This is meant to give the student practice in answering questions of the format that will appear on Exam 5. Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.

Source:
Werner, Geoff and Claudine Modlin. Basic Ratemaking. Casualty Actuarial Society. 2009. Chapter 6, pp. 100-101.

Original Problems and Solutions from The Actuary's Free Study Guide

Problem S5-41-1. You are given the following information:
The state average weekly wage (SAWW) is $1100.

The compensation rate for an injured worker is 80% of the worker's pre-injury wage.

The state-mandated minimum indemnity benefit is 80% of the SAWW, and the maximum indemnity benefit is 120% of the SAWW. Assume that all of the workers below get injured. What will be the total amounts in benefits received by workers subject to the minimum benefit?

Ratio to SAWW......Number of Workers.......Total Weekly Wages

Less than 25%..........................2............................$430

25%-50%................................12...........................$3600

50%-75%................................12...........................$7500

75%-100%..............................19..........................$15000

100%-125%............................18..........................$21000

125%-150%............................13..........................$21000

>150%....................................13...........................$80000

Solution S5-41-1. We first consider how many workers would be subject to the minimum benefit. These are workers who would otherwise be entitled to less than 80% of the SAWW in benefits. Since the compensation rate is 80% of the pre-injury wage, the largest percentage of the SAWW that workers who are subject to the minimum benefit would earn before injury is 0.8/0.8 = 1 = 100%. So, the 2 + 12 + 12 + 19 = 45 workers who earn below 100% of the SAWW will be subject to the minimum benefit of $1100*0.8 = $880, and these workers combined would receive 880*45 = $39,600.

Problem S5-41-2. You are given the following information:
The state average weekly wage (SAWW) is $1100.

The compensation rate for an injured worker is 80% of the worker's pre-injury wage.

The state-mandated minimum indemnity benefit is 80% of the SAWW, and the maximum indemnity benefit is 120% of the SAWW. Assume that all of the workers below get injured. What will be the total amounts in benefits received by workers subject to the maximum benefit?

Ratio to SAWW......Number of Workers.......Total Weekly Wages

Less than 25%.........................2............................$430

25%-50%................................12...........................$3600

50%-75%................................12...........................$7500

75%-100%..............................19..........................$15000

100%-125%............................18..........................$21000

125%-150%............................13..........................$21000

>150%....................................13...........................$80000

Solution S5-41-2. We consider how many workers would be subject to the maximum benefit. These are workers who would otherwise be entitled to more than 120% of the SAWW in benefits, which corresponds to a pre-injury wage level of at least 1.2/0.8 = 1.5 = 150% of the SAWW. Thus, 13 workers are subject to the maximum benefit, which is 1.2*1100 = $1320, leading to a total payout for these workers of 13*1320 = $17,160.

Problem S5-41-3. You are given the following information:
The state average weekly wage (SAWW) is $1100.

The compensation rate for an injured worker is 80% of the worker's pre-injury wage.

The state-mandated minimum indemnity benefit is 80% of the SAWW, and the maximum indemnity benefit is 120% of the SAWW. Assume that all of the workers below get injured. What will be the total amounts in benefits received by all these workers?

Ratio to SAWW......Number of Workers.......Total Weekly Wages\

Less than 25%..........................2............................$430

25%-50%................................12...........................$3600

50%-75%................................12...........................$7500

75%-100%..............................19..........................$15000

100%-125%............................18..........................$21000

125%-150%............................13..........................$21000

>150%....................................13...........................$80000

Solution S5-41-3. In Solution S5-41-1 and Solution S5-41-2, we already determined that the 45 workers earning less than 100% of the SAWW will receive $39,600 in benefits, while the 13 workers earning more than 150% of the SAWW will receive $17,160 in benefits. The combined wages of the workers earning between 100% and 150% of the SAWW are 21000 + 21000 = 42000. Because the compensation rate is 80% of the pre-injury wage, these workers will receive 0.8*42000 = $33,600, leading to a total of 39600 + 33600 + 17160 = $90,360 in benefits.

Problem S5-41-4. You are given the following information:
The state average weekly wage (SAWW) is $1100.

The compensation rate for an injured worker is 80% of the worker's pre-injury wage.

The state-mandated minimum indemnity benefit is 80% of the SAWW, and the maximum indemnity benefit is 120% of the SAWW.

A new law increases the minimum indemnity benefit to 100% of the SAWW.

Assume that all of the workers below get injured. What will be the total amounts in benefits received by all these workers under the new benefit structure?

Ratio to SAWW......Number of Workers.......Total Weekly Wages

Less than 25%.........................2............................$430

25%-50%................................12...........................$3600

50%-75%................................12...........................$7500

75%-100%..............................19..........................$15000

100%-125%............................18..........................$21000

125%-150%............................13..........................$21000

>150%....................................13...........................$80000

Solution S5-41-4. The new change affects the number of workers receiving the minimum benefit, but does not affect the number of workers receiving the maximum benefit, of which the total payout remains at $17,160 (from Solution S5-41-2). A worker whose benefit is 100% of the SAWW would have received 1/0.8 = 1.25 = 125% of the SAWW prior to injury. This means that the number of workers receiving the minimum benefit under the new structure has grown from 45 to 45 + 18 = 63, each of whom receives the $1100 SAWW as a benefit, leading to a total payout of 63*1100 = $69,300. The remaining workers, those earning between 125% and 150% of the SAWW, will receive 21000*0.8 = $16,800 in benefits, resulting in total benefits of 69300 + 16800 + 17160 = $103,260.

Problem S5-41-5. You are given the following information:
The state average weekly wage (SAWW) is $1100.

The compensation rate for an injured worker is 80% of the worker's pre-injury wage.

The state-mandated minimum indemnity benefit is 80% of the SAWW, and the maximum indemnity benefit is 120% of the SAWW.

A new law increases the minimum indemnity benefit to 100% of the SAWW.

Assume that all of the workers below get injured. What is the direct effect (percentage decrease or increase) on the benefit level because of this change in law? Assume that nothing else changes.

Ratio to SAWW......Number of Workers.......Total Weekly Wages

Less than 25%..........................2............................$430

25%-50%................................12...........................$3600

50%-75%................................12...........................$7500

75%-100%..............................19..........................$15000

100%-125%............................18..........................$21000

125%-150%............................13..........................$21000

>150%....................................13...........................$80000

Solution S5-41-5. In Solution S5-41-3, we found that the total benefits prior to the law change were $90,360; after the law change, they would be $103,260. The percentage change is simply 100*(103260/90360 - 1) = an increase of 14.2762284%.

See other sections of The Actuary's Free Study Guide for Exam 5.