Step 1
Write the annuity formula
[tex]A=\frac{P[(1+\frac{r}{n})^{nt}-1]}{\frac{r}{n}}[/tex]where;
[tex]\begin{gathered} t=68-23=45 \\ P=310 \\ r=\frac{5.8}{100}=0.058 \\ A=? \\ n=12 \end{gathered}[/tex]Step 2
Find how much money will he have saved upon retirement at the age of 68.
[tex]A=\frac{310[(1+\frac{0.058}{12})^{12\times45}-1]}{\frac{0.058}{12}}[/tex][tex]\begin{gathered} A=\frac{310[(1+\frac{0.058}{12})^{540}-1]}{\frac{0.058}{12}} \\ A=\frac{310\left(\left(1+\frac{0.058}{12}\right)^{540}-1\right)\cdot\:12}{0.058} \\ A=\frac{3720\left(\left(\frac{0.058}{12}+1\right)^{540}-1\right)}{0.058} \\ A=\frac{46551.40463}{0.058} \\ A=802610.42468 \\ A\approx\text{\$802610.42} \\ \end{gathered}[/tex]
