question 3 of 10\nif your starting salary is $50,000 and you receive a 4% increase at the end of every year…

question 3 of 10\nif 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?\nround your answer to the nearest whole dollar, and express your answer without using commas.

question 3 of 10\nif 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?\nround your answer to the nearest whole dollar, and express your answer without using commas.

Answer

Explanation:

Step1: Identify the formula for a geometric - series sum

The salary forms a geometric series. The formula for the sum of a geometric series $S_n=\sum_{k = 0}^{n - 1}a\cdot r^k=\frac{a(1 - r^n)}{1 - r}$, where $a$ is the first - term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = 50000$, $r=1 + 0.04=1.04$, and $n = 16$.

Step2: Substitute the values into the formula

$S_{16}=\frac{50000(1 - 1.04^{16})}{1 - 1.04}$. First, calculate $1.04^{16}$. Using the formula $y = a^x$, where $a = 1.04$ and $x = 16$, we have $1.04^{16}\approx1.872981$. Then, $1-1.04^{16}=1 - 1.872981=-0.872981$. And $1 - 1.04=-0.04$. So, $S_{16}=\frac{50000\times(- 0.872981)}{-0.04}$.

Step3: Calculate the sum

$S_{16}=\frac{-43649.05}{-0.04}=1091226.25$. Rounding to the nearest whole dollar, we get $1091226$.

Answer:

1091226