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Geometric sequence help.

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e. An employee has a starting salary of \$20,000 and can choose from two salary options:

Option 1: A salary increase by 5% each year.

Option 2: A guaranteed increase of \$1,000 each year.

i. Which option is initially more beneficial?

ii. Which option is more beneficial after 10 years of employment?

Feb 24, 2019

#1
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Initially, they are both the same    after 1 year he will get a \$1000 raise with each method.    After the first year, the 5% one begins to be better and better due to compounding.

At 10 years the 5% option will be paying him    20000(1.05)^10 = 32577.89 / yr

the 1000 increase per year will only be paying  30,000      (20000 + 1000*10)

Feb 24, 2019
#2
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i.  5% of 20,000 is 1,000, so initially the options are equal

ii.  Take Option 1.  Not only is it more beneficial after 10 years, it's more beneficial after only 2 years.   After the first year, the salary is 21,000 so calculating the salary increase on 21,000 the second year the increase would be 5% of 21,000 which is 1,050.  That made the salary 22,050 and the next increase would be 5% of 22,050 which is 1,102.50.

Feb 24, 2019