Given
[tex]\begin{gathered} d=\text{ the regular deposit =40} \\ r=0.045\text{ \% \lparen4.5\%\rparen} \\ k=k=12\text{ }compounds/depositsperyear \\ t=65years-34years=31years \end{gathered}[/tex]
Explanation
We can then use the annuity formula to find the amount the person will have at age 65.
[tex]P_N=\frac{d((1+\frac{r}{k})^{Nk}-1)}{\frac{r}{k}}[/tex]
Therefore, we will have;
[tex]\begin{gathered} P_{31}=\frac{40((1+0.045\/12)^{31\times12}-1)}{\frac{0.045}{12}} \\ =\frac{40\left(\left(\frac{0.045}{12}+1\right)^{372}-1\right)}{\frac{0.045}{12}} \\ =\frac{40\left(\left(1+\frac{0.045}{12}\right)^{372}-1\right)\times\:12}{0.045} \\ =\frac{480\left(1.00375^{372}-1\right)}{0.045} \\ =\frac{1451.74110}{0.045} \end{gathered}[/tex]
