Respuesta :
ANSWER
$54,437,972
EXPLANATION
We have that she wants to deposit $500 every month in the account at a compound interest rate of 5.85%.
She will do that for 17 years.
To find the amount of interest after 17 years, we will use the formula:
[tex]I\text{ = }P(1\text{ + }r)^t\text{ - P}[/tex]where P = principal = $500
r = monthly interest rate = 5.85%
t = number of months
To find t, we will multiply 17 years by 12 months (12 months in a year):
t = 17 * 12 = 204 months
Therefore, we have that, the interest after 17 years is:
[tex]\begin{gathered} I\text{ = }500(1\text{ + }\frac{5.85}{100})^{204}-500=500(1+0.0585)^{204}\text{ - 500} \\ I=500(1.0585)^{204}\text{ - 500 = (500}\cdot108876.944)\text{ - 500} \\ I\text{ = 54438}472\text{ - 500} \\ I\text{ = \$54,437,972} \end{gathered}[/tex]Therefore, the interest will be $54,437,972
