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HUGGIE BUGGIE!!!'s question at Yahoo! Answers regarding calculating a sum

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MarkFL

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Feb 24, 2012
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Here is the question:

Math Homework HELP! PLEASE!?


If your starting salary were $50,000 and you received a 4% increase at the end of every year for 15 years, what would be the total amount, in dollars, you would have earned over the first 16 years that you worked?

I have no idea how to get the answer to this please help me!

I have to round my answer to the nearest dollar
I have posted a link there to this thread so the OP can see my work.
 
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MarkFL

Administrator
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Feb 24, 2012
13,775
Hello HUGGIE BUGGIE!!!,

Your salary $S$ for the $k$th year in dollars is:

\(\displaystyle S_k=50000\left(\frac{26}{25} \right)^{k-1}\)

And hence, the sum total $T$ of the money earned during the first $n$ years is:

\(\displaystyle T_n=50000\sum_{k=1}^{n}\left(\frac{26}{25} \right)^{k-1}=50000\sum_{k=0}^{n-1}\left(\frac{26}{25} \right)^{k}\)

Using the formula:

\(\displaystyle \sum_{k=0}^{n}r^k=\frac{r^{n+1}-1}{r-1}\)

we may write:

\(\displaystyle T_n=50000\left(\frac{\left(\dfrac{26}{25} \right)^n-1}{\frac{26}{25}-1} \right)=1250000\left(\left(\frac{26}{25} \right)^n-1 \right)\)

Thus, the money earned during the first 16 years is:

\(\displaystyle T_{16}=1250000\left(\left(\frac{26}{25} \right)^{16}-1 \right)=\frac{325210856544670578706416}{298023223876953125}\approx1091227\)