Answer
Jean's account will have a balance of $\$4150$ after about 10 years.
Work Step by Step
Jean invests $\$2300$ in a retirement account with a $6\%$ interest compounded annually.
That means every year, Jean's account would increase by $6\%$ of the amount available.
For example, after first year, Jean's account would increase by $6\%$ of $\$2300$; after second year, Jean's account would increase by $6\%$ of $[\$2300\times(106\%)]$ and so on.
Therefore, if we take $t$ to be the amount of time for Jean's account to reach $\$4150$, we have this equation:
$$2300\times(1.06)^t=4150$$
$$(1.06)^t=1.804$$
Here, we use graphing calculator and find out that $$t\approx10.129\approx10(years)$$
Therefore, we can conclude that Jean's account will have a balance of $\$4150$ after about 10 years.
