Question

You are interviewing for a job and receive two offers:

A: \(20,000 to start, with guaranteed annual increases of 6% for the first 5 years

B: \)22,000 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)?

Short answer

The first job is the better option if the goal is to make as much as possible after 5 years.

The first job will be the better option to make as much money as possible over the contract (5 years).

Step-by-step solution

Step 1. Given information

You are interviewing for a job and receive two offers:

A: $20,000 to start, with guaranteed annual increases of 6% for the first 5 years

B: $22,000 to start, with guaranteed annual increases of 3% for the first 5 years

Step 2. Better Option

Let $a$represents the first job and $b$represents the second job

Let starting wage of the first job be $a_0=20,000$with an annual increase of $6\%$for the first 5 years

And the starting wage of the second bob be $b_0=\$22,000$with an annual increase of 3% for the first 5 years.

The sequence will be

$$\begin{gathered} a_n=a_{n-1}+a_{n-1}(0.06) \\ {b}_n=b_{n-1}+b_{n-1}(0.03) \end{gathered}$$

The first 5 terms of both sequences are

n	$a_n$		n	$b_n$
1	21200.00		1	22660.00
2	22472.00		2	23339.80
3	237320.32		3	24039.99
4	25249.54		4	24761.19
5	26764.51		5	25504.03

From the above table, we conclude that $26764.51>25504.03$

Therefore the first job is the better option if the goal is to make as much as possible after 5 years.

After 5 years there will be no annual increase for both the jobs.

Therefore the first job will be the better option to make as much money as possible over the contract (5 years)