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Wen takes a job with a starting salary of $100,000 for the first year. She earns a 3% increase each year. What does S5 represent?

User Jennyfer
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2 Answers

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I'm assuming S5 is the salary after 5 years? you should include that when asking a question.

y = years
S = Salary after y years

equation:
S(y) = 100,000(1.03)^y

S(5) = 100,000(1.03)^5
S(5) = 115,927.41

User Henningsson
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1 vote

Answer:

The sum of 5 year salary is $53,00,000.

Explanation:

Given : Wen takes a job with a starting salary of $100,000 for the first year. She earns a 3% increase each year.

To find : What does
S_5 represent?

Solution :

We have to find the sum of 5 year salaries

We apply geometric series sum formula,


S_n=(a_1(1-r^n))/(1-r)

Where,
a_1 is the initial or first number,

we have given
a_1=100,000

r is the common ratio,

We have given she earns a 3% increase each year = 1+0.03=1.03

r=1.03

n is the number of terms,

n=5

Substitute the value in the formula,


S_n=(a_1(1-r^n))/(1-r)


S_5=(1000000(1-(1.03)^5))/(1-1.03)


S_5=(1000000(1-1.159))/(1-1.03)


S_5=(1000000(-0.159))/(-0.03)


S_5=(−159000)/(-0.03)


S_5=5300000

Therefore, The sum of 5 year salary is $53,00,000.

User Tom Burrows
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