The formula for the future value of annuity is given by
Where,
[tex]\begin{gathered} A=\text{regular deposits= \$1900} \\ r=2.4\text{ \%=}\frac{\text{2.4}}{100}=0.024 \\ T=\text{ number of years =17} \\ m=\text{frequency}=4 \end{gathered}[/tex]
By substituting the values, we will have
[tex]FV_{OA}=A\lbrack(\frac{1+\frac{r}{m})^{mT}-1}{\frac{r}{m}}\rbrack[/tex]
Therefore,
We will have
[tex]\begin{gathered} FV_{OA}=A\lbrack(\frac{(1+\frac{r}{m})^{mT}-1}{\frac{r}{m}}\rbrack \\ FV_{OA}=1900\frac{\lbrack(1+\frac{0.024}{4})^{4\times17})_{}-1\rbrack}{\frac{0.024}{4}} \end{gathered}[/tex][tex]\begin{gathered} FV_{OA}=1900\frac{\lbrack(1+\frac{0.024}{4})^{4\times17})_{}-1\rbrack}{\frac{0.024}{4}} \\ FV_{OA}=\frac{1900\lbrack(1+0.006)^{68}-1\rbrack}{0.006} \\ FV_{OA}=\frac{1900\lbrack(1.006)^{68}-1\rbrack}{0.006} \\ FV_{OA}=\frac{1900(0.501975)}{0.006} \\ FV_{OA}=\frac{953.7525}{0.006} \\ FV_{OA}=\text{ \$}158,958.75 \\ \text{Appro}\xi\text{mately to the nearest dollar will be} \\ FV_{OA}=\text{ \$158,959} \end{gathered}[/tex]
Therefore,
The future value of the annuity = $158,959
