Question

question 2 of 10
if your starting salary is $50,000 and you receive a 4% increase at the end of every year, what is the total amount, in dollars, you will earn over the first 16 years that you work?
round your answer to the nearest whole dollar, and express your answer without using commas.

Explanation:

Step1: Identify the series type

This is a geometric series problem. The first term \(a = 50000\), the common ratio \(r=1 + 0.04=1.04\), and the number of terms \(n = 16\). The formula for the sum of a geometric series is \(S_n=\frac{a(r^n - 1)}{r - 1}\) (when \(r
eq1\)).

Step2: Substitute values into the formula

Substitute \(a = 50000\), \(r = 1.04\), and \(n=16\) into the formula:

$$S_{16}=\frac{50000\times(1.04^{16}-1)}{1.04 - 1}$$

Step3: Calculate \(1.04^{16}\)

Using a calculator, \(1.04^{16}\approx1.872981\)

Step4: Calculate the numerator

\(50000\times(1.872981 - 1)=50000\times0.872981 = 43649.05\)

Step5: Calculate the denominator

\(1.04-1 = 0.04\)

Step6: Calculate the sum

\(S_{16}=\frac{43649.05}{0.04}=1091226.25\)

Step7: Round to the nearest whole dollar

Rounding \(1091226.25\) to the nearest whole dollar gives \(1091226\)

Answer:

1091226