Critical Thinking You are interviewing for a job and receive...

Critical Thinking You are interviewing for a job and receive two offers for a five-year contract: A: $$\$ 40,000$$ to start, with guaranteed annual increases of $6 \%$ for the first 5 years $$B: \$ 44,000$$ to start, with guaranteed annual increases of $3 \%$ for the first 5 years Which offer is better if your goal is to be making as much as possible after 5 years? Which is better if your goal is to make as much money as possible over the contract (5 years)?

Critical Thinking You are interviewing for a job and receive two offers for a five-year contract:
A: $$\$ 40,000$$ to start, with guaranteed annual increases of $6 \%$ for the first 5 years
$$B: \$ 44,000$$ to start, with guaranteed annual increases of $3 \%$ for the first 5 years
Which offer is better if your goal is to be making as much as possible after 5 years? Which is better if your goal is to make as much money as possible over the contract (5 years)?

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Key Concepts

Cumulative Earnings Assessment

Cumulative earnings assessment involves calculating the total amount of money earned over the duration of the contract by summing up the yearly salaries. This analysis is important when comparing job offers because it shows the overall financial gain over the course of the contract, not just the terminal salary after the last year.

Future Value Calculation

Future value calculation involves determining the value of an initial amount after a series of compound increases over a given number of periods. In salary comparisons, this concept is used to project what a salary will be at the end of a contract, using the formula P*(1 + r)^n, where P is the starting salary, r is the annual raise percentage, and n is the number of years.

Compound Growth

Compound growth refers to the process where a quantity increases exponentially over time by a constant percentage rate. In the context of salary offers, it means that each year’s pay increase is applied to the new, already increased salary, resulting in an accelerating growth over time.

Transcript

00:01 So you have two options.

00:02 You can either be paid starting salary of $20 ,000 and get a 6 % increase for five years.

00:12 And you can also have a job that has $22 ,000 and getting a 3 % increase.

00:18 So if you just wanted to figure out how much you'll make after five years, this is a geometric with $20 ,000 times 1 .06, to the fourth power, that would be your fifth year salary.

00:34 And let's see what that comes out to be.

00:37 20 ,000 times 1 .06 to the fourth power.

00:44 You would end up making the whopping $25 ,249.

00:49 And 54 cents over that in that fifth year.

00:54 If you had this scheme, you would have 22 ,000 times 1 .03 to the fourth power because you would get four increases in pay.

01:07 And we can just go up in second entry, and i can just go back and change that.

01:13 So that becomes a 22 ,000 and change that increase to 1 .03.

01:18 And you would be making $24 ,761 in 19 cents during that fifth year.

01:25 So if you just want to look at how much you will earn in the fifth year, you would want to use choice a.

01:34 Now, on the other hand, if you accumulatively want to know how much money you would have earned over the whole period of time, let's do a sum.

01:42 So we'll do the sum in blue...

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