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### Salary at 5 Percent Yearly Increase

Date: 9/11/96 at 16:49:53
From: Anonymous
Subject: Salary at 5 percent Yearly Increase

Dr. Math,

If Martin started with a company at an annual salary of \$18,000, and
he gets an increase of 5 percent at the end of every year, at this
growth rate, what would Martin's salary be in his 30th year with his
company?

I started with the formula S (sub n)=18,000(1.05)^(n-1)

What do I supply for n?  Also, what would be the first 3 terms of the
sequence?

Thank you,
Emily Pawlosky

Date: 9/11/96 at 18:52:50
From: Doctor Tom
Subject: Re: Salary at 5 percent Yearly Increase

Hi Emily,

Here's how I'd approach the problem (I'll use '*' for multiplication
and '^' to indicate exponentiation):

In year 1, he earns 18000
In year 2, he earns 18000*1.05
In year 3, he earns 18000*(1.05)^2
In year 4, he earns 18000*(1.05)^3

and so on, so during the 30th year, he'll be earning 18000*(1.05)^29.

I plugged this into my calculator, and it's \$74090.44 in the 30th
year.

I don't know what you mean by the first 3 terms of this, unless
the question was, "how much total money does he earn in all 30
years?"  If that's the question, the answer is:

18000 + 18000*(1.05)^1 + 18000*(1.05)^2 + ... + 18000*(1.05)^29.

-Doctor Tom,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/

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