calculus question

Question

A person's annual salary starts out at $50000. In scenario 1, the person receives an annual raise of $3500.

What is her annual salary after 9 years? After 27 years? 

In scenario 2 the person receives an annual raise of 3.5%.

What is her annual salary after 9 years? After 27 years? 

Answer 1

Here is how I would suggest you think about it.

In scenario 1: every year it adds 3500 onto the salary. Meaning the after 1 year it would be 50000 + 3500, after 2 years it would be 50000 + 3500 + 3500 which is 50000 + 2*3500. If you follow this pattern, the answer will be right in front of you.

In scenario 2: This time its in terms of percentage. But the concept is the same, try to find the patterns. 3.5 % is 0.035, so after 1 year it would be 50000 + 50000*0.035. well this is nasty : [

Lets tidy it up 50000 + 50000*0.035 = 50000*(1+0.035). Better!

Now after 2 years, it would be adding 3.5% based on first year's ending salary which is 50000*(1+0.035).

So, 50000*(1+0.035) + 50000*(1+0.035)*0.035 = 50000*(1+0.035)²

Do you start to see the pattern now?