kadeem was offered a job that paid a salary of $31,500 in its first year. the salary was set to increase by…

kadeem was offered a job that paid a salary of $31,500 in its first year. the salary was set to increase by 6% per year every year. if kadeem worked at the job for 22 years, what was the total amount of money earned over the 22 years, to the nearest whole number?

kadeem was offered a job that paid a salary of $31,500 in its first year. the salary was set to increase by 6% per year every year. if kadeem worked at the job for 22 years, what was the total amount of money earned over the 22 years, to the nearest whole number?

Answer

Explanation:

Step1: Identify the formula for the sum of a geometric series

The salary forms a geometric - series with first term $a = 31500$, common ratio $r=1 + 0.06=1.06$, and number of terms $n = 22$. The sum of a geometric series is given by $S_n=\frac{a(r^n - 1)}{r - 1}$ when $r\neq1$.

Step2: Substitute the values into the formula

Substitute $a = 31500$, $r = 1.06$, and $n = 22$ into the formula $S_{22}=\frac{31500\times(1.06^{22}-1)}{1.06 - 1}$. First, calculate $1.06^{22}$. Using a calculator, $1.06^{22}\approx3.54777$. Then $1.06^{22}-1\approx3.54777 - 1=2.54777$. Next, $1.06 - 1 = 0.06$. So, $S_{22}=\frac{31500\times2.54777}{0.06}$.

Step3: Calculate the sum

$31500\times2.54777 = 31500\times(2 + 0.5+0.04 + 0.007+0.0007+0.00007)\approx80254.755$. Then $\frac{80254.755}{0.06}=1337579.25$.

Answer:

$1337579$