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?
iii. Explain your reasoning
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)
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.