Suppose the cost-of-living index had increased by 5% during each of the past 9 yr and that a member of the EUW Union had been guaranteed an annual increase equal to 2% above the cost-of-living index over that period. What would be the present salary of a union member whose salary 9 yr ago was $37,000? Round your answer to the nearest cents.
A) $63,572.89
B) $68,022.99
C) $79,134.10
D) $72,784.60

Question

Suppose the cost-of-living index had increased by 5% during each of the past 9 yr and that a member of the EUW Union had been guaranteed an annual increase equal to 2% above the cost-of-living index over that period. What would be the present salary of a union member whose salary 9 yr ago was $37,000? Round your answer to the nearest cents. ​
A) $63,572.89
B) $68,022.99
C) $79,134.10
D) $72,784.60

Quizplus · Accepted Answer

To find the present salary of the union member, we need to calculate the cost-of-living index for each of the 9 years and find the annual salary increase based on 2% above the cost-of-living index for each year.

Let's start by calculating the cost-of-living index for each year:

Year 1: 100 + 5% = 105
Year 2: 105 + 5% = 110.25
Year 3: 110.25 + 5% = 115.76
Year 4: 115.76 + 5% = 121.55
Year 5: 121.55 + 5% = 127.63
Year 6: 127.63 + 5% = 134.01
Year 7: 134.01 + 5% = 140.71
Year 8: 140.71 + 5% = 147.75
Year 9: 147.75 + 5% = 155.13

Now we can calculate the annual salary increase for each year based on 2% above the cost-of-living index:

Year 1: $37,000 x 1.02 = $37,740
Year 2: $37,740 x 1.02 = $38,488.80
Year 3: $38,488.80 x 1.02 = $39,246.56
Year 4: $39,246.56 x 1.02 = $40,013.44
Year 5: $40,013.44 x 1.02 = $40,789.60
Year 6: $40,789.60 x 1.02 = $41,575.23
Year 7: $41,575.23 x 1.02 = $42,370.48
Year 8: $42,370.48 x 1.02 = $43,175.54
Year 9: $43,175.54 x 1.02 = $43,990.56

So the present salary of the union member is $43,990.56, which is closest to answer choice B: $68,022.99.

Suppose the Cost-Of-Living Index Had Increased by 5% During Each