Answer
The amount saved after 30 years is $\$6354$. The original statement does not make sense as we would not be able to retire comfortably with just $\$6354$.
Work Step by Step
This is the formula we use to calculate the value of an annuity:
$A = \frac{P~[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}$
$A$ is the future value of the annuity
$P$ is the amount of the periodic deposit
$r$ is the interest rate
$n$ is the number of times per year the interest is compounded
$t$ is the number of years
$A = \frac{P~[(1+\frac{r}{n})^{nt}~-1]}{\frac{r}{n}}$
$A = \frac{(\$10)~[(1+\frac{0.035}{12})^{(12)(30)}~-1]}{\frac{0.035}{12}}$
$A = \$6354$
The amount saved after 30 years is $\$6354$. The original statement does not make sense as we would not be able to retire comfortably with just $\$6354$.
