Answer :
Answer:
Antoinette's parents paid $ 70000 by the time she left the school.
Step-by-step explanation:
Antoinette's parents paid at the beginning ([tex]t = 0[/tex]) $ 6230, and each year paid annual fees including increases seven times. ([tex]0 <t \leq 7[/tex]) We find that annual fee paid at a given year is represented by the following formula:
[tex]C(t) = C_{o}\cdot \left(1+\frac{r}{100} \right)^{t}[/tex]
Where:
[tex]C_{o}[/tex] - Initial annual fees, measured in US dollars.
[tex]C(t)[/tex] - Current annual fees, measured in US dollars.
[tex]r[/tex] - Yearly increase rate, dimensionless.
If we know that [tex]C_{o} = \$\,6230[/tex] and [tex]r =9.5[/tex], first 8 annual fees paid by Antoinette's parents are:
[tex]C(0) = \$\,6230[/tex]
[tex]C(1) =\$\,6821.85[/tex]
[tex]C(2) = \$\,7469.93[/tex]
[tex]C(3) = \$\,8179.57[/tex]
[tex]C(4) = \$\,8956.63[/tex]
[tex]C(5) = \$\,9807.51[/tex]
[tex]C(6) = \$\,10739.22[/tex]
[tex]C(7) = \$\,11759.45[/tex]
Now, we sum each yearly fees to determine the total paid by Antoinette's parents when she leaves the school at the end of the 8th year.
[tex]C_{T} = C(0) +C(1)+C(2) + C(3)+C(4)+C(5)+C(6)+C(7)[/tex]
[tex]C_{T} = \$\,6230+\$\,6821.85+\$\,7469.93+\$\,8179.57+\$\,8956.63+\$\,9807.51+\$\,10739.22+\$\,11759.45[/tex]
[tex]C_{T} = \$\,69964.16[/tex]
Antoinette's parents paid $ 70000 by the time she left the school.