Respuesta :
The rule of the FV (future value) is
[tex]FV=P\frac{(1+i)^n-1}{i}[/tex]P is the value each month
i is the rate divided by 12 month
n = number of years x 12 months
Since the deposit every month is $1643, then
[tex]P=1643[/tex]Since the annuity rate is 4.5%, then
[tex]\begin{gathered} i=\frac{4.5}{12}=0.375\text{ \%} \\ i=\frac{0.375}{100}=0.00375 \end{gathered}[/tex]Since the number of years is 11 years, then
[tex]\begin{gathered} n=11\times12 \\ n=132 \end{gathered}[/tex]Substitute them in the rule above
[tex]\begin{gathered} FV=1643\frac{(1+0.00375)^{132}-1}{0.00375} \\ FV=279958.5032 \end{gathered}[/tex]The account will have $279,959 after 11 years to the nearest dollar
To find the interest subtract $1643 x 132 months from the FV
[tex]\begin{gathered} I=FV-n\times P \\ I=279959-132\times1643 \\ I=63083 \end{gathered}[/tex]The amount of interest is $63,083 to the nearest dollar
