Answer
The money she made during her fourth year of business (n = 4) is $\$39,930$
Her total earnings during the first four years is $\$139,230$
Work Step by Step
The situation can be represented by a geometric series with $a_{1} = \$30000$ and $r = (1 + 10\%) = 1.1$ including the initial amount made in the first year, which the general term is $a_{n} = 30000(1.1)^{n-1}$ and $n$ is the number of year
The money she made during her fourth year of business (n = 4) is
$a_{4} = 30000(1.1)^{4-1} = \$39,930$
Her total earnings during the first four years is
$\sum\limits_{n=1}^4 a_{n} = \sum\limits_{n=1}^4 30000(1.1)^{n-1}$
= $\frac{30000(1 - 1.1^4)}{(1 - 1.1)}$
= $\$139,230$
