Solve the problem.
-A job pays a salary of 27,000 the first year. During the next 9 years, the salary increases by 5% each year. What is the salary for the 10th year? What is the total salary over the 10-year period? (Round to the nearest cent.)
A)$41,885.86; $339,603.10
B)$43,980.15; $383,583.25
C)$41,885.86; $297,717.24
D)$43,980.15; $297,737.24

Question

Quizplus · Accepted Answer

The salary for the 10th year is calculated using the formula for compound interest: $P(1 + r)^n$, where $P = 27,000$, $r = 0.05$, and $n = 9$. This gives $27,000(1 + 0.05)^9 = 41,885.86$. The total salary over the 10-year period is the sum of a geometric series, which can be calculated using the formula for the sum of a geometric series: $S_n = P \frac{(1 - r^n)}{1 - r}$, where $P = 27,000$, $r = 1.05$, and $n = 10$. This gives a total of $339,603.10$.

Solve the Problem. -A Job Pays a Salary of 27,000 the First Year