# Cassandra starts working for a company for an annual salary of $30,000. If she earns a 2% raise at the end of each year, what will her total earnings be after five years. I have to determine the...

Cassandra starts working for a company for an annual salary of $30,000. If she earns a 2% raise at the end of each year, what will her total earnings be after five years. I have to determine the type of series----identify the first term--the common difference or the common ratio, and the number of terms--the general formula to use to substitute and simplify.

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Cassandra starts working for a company for an annual salary of $30,000. She is given a 2% raise at the end of each year.

Her earnings after n year of working is given by `30000*(1+2/100)^n`

`30000*(1+2/100)^n` is a term of a geometric series with first term 30000 and common ratio 1.02.

The sum of n terms of a geometric series is `(A*(r^n - 1))/(r - 1)` .

Here, A = 30000, r = 1.02 and n = 5

The required sum is `30000*(1.02^5 - 1)/(1.02 - 1)`

= $156,121.2

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`A = P(1+r/n)^(t*n)`

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$30,000 is the initial amount (P)

1 + r stands for the intial amount plus the the rate, and much it is compounded.

t*n stands for the number of years times the number of payments

If she earns a 2% raise, that means she the rate is .02%

`A = 30,000 (1+.02/1)^(5*1)`

`A = 30,000(1.02)^5`

`A = $33,122.42` this is the amount of money after 5 years in the bank

The type of series is **geometric series **because the common formula for geometric is `A_n = A_1 + r^(n-1)`

The first term in the series is 30,000, and the ratio is 1.2. It is not .2, but 1.2, because you are increasing, and it is the overall total.

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To find what their salary would be after 5 years, starting at 30000 per year, with a 2% raise each year, you would use the formula 30000 (1 + 2/100) ^ n.

Your first term would be 30000 and the common ratio is (1 + 2/100) or 1.02. N would be 5, for 5 years.

I am not really sure how to solve geometric series since it has been a while but I put a couple links that might help you :)

**Sources:**