a woman makes $25,000 during the first year of her new job at city hall. each year she receives an 8% raise…

a woman makes $25,000 during the first year of her new job at city hall. each year she receives an 8% raise. find her total earnings during her first four years on the job.\na $146,665.02\nb $118,745.60\nc $100,000.00\nd $112,652.80

a woman makes $25,000 during the first year of her new job at city hall. each year she receives an 8% raise. find her total earnings during her first four years on the job.\na $146,665.02\nb $118,745.60\nc $100,000.00\nd $112,652.80

Answer

Explanation:

Step1: Identify the formula for a geometric - series sum

The first - year salary $a = 25000$, the common ratio $r=1 + 0.08=1.08$, and $n = 4$ (number of years). The sum of a geometric series $S_n=\frac{a(r^n - 1)}{r - 1}$.

Step2: Substitute the values into the formula

$S_4=\frac{25000(1.08^4 - 1)}{1.08 - 1}$. First, calculate $1.08^4=1.08\times1.08\times1.08\times1.08 = 1.36048896$. Then, $1.08^4-1=1.36048896 - 1=0.36048896$. And $1.08 - 1 = 0.08$.

Step3: Calculate the sum

$S_4=\frac{25000\times0.36048896}{0.08}$. $25000\times0.36048896 = 9012.224$. $\frac{9012.224}{0.08}=112652.8$.

Answer:

D. $112,652.80$