which salary plan would you prefer a) you are offered job A with a starting salary of $24,000.each year for 10 years you will be given a 4% raise. b) you offered job B with a starting of $24000. each year for 10 years you will be given a $1000 raise.
Plan A: geometric series with a = 24000 , r = 1.04
sum(10) = 24000(1.04^10 - 1)/.04 = $288 146.57
plan B: arithmetic sequence: a = 24000, d = 1000
sum(10) = (10/2)(48000 + 9000) = $285 000.00
what do you think?
At 4%, the first year raise will be $960, second will be $998.40, third year, $10,383.36. Take it from there.
To determine which salary plan is preferable, we need to compare the total earnings over the 10-year period for both job A and job B.
For job A:
Starting salary: $24,000
Annual raise: 4%
To calculate the annual salary for each year, we need to add the 4% raise to the previous year's salary. Let's do the calculations:
Year 1: $24,000
Year 2: $24,000 + (4% of $24,000) = $24,000 + $960 = $24,960
Year 3: $24,960 + (4% of $24,960) = $24,960 + $998.40 = $25,958.40
We can continue this calculation for each year and add up the total earnings over the 10-year period.
For job B:
Starting salary: $24,000
Annual raise: $1,000
To calculate the annual salary for each year, we simply need to add the $1,000 raise to the previous year's salary. Let's do the calculations:
Year 1: $24,000
Year 2: $24,000 + $1,000 = $25,000
Year 3: $25,000 + $1,000 = $26,000
We can continue this calculation for each year and add up the total earnings over the 10-year period.
After calculating the earnings for both salary plans, we can compare the totals to determine which plan provides a higher total earnings over the 10-year period.