Question

School fees for a popular high school have been increasing by 9.5% per year. When Antoinette started the school, the annual fees were $6230. By the time Antoinette leaves the school 8 years later, how much have her parents paid in school fees in total? Give your answer to the nearest $100.

Answer 1

Answer:

Antoinette's parents paid $ 70000 by the time she left the school.

Step-by-step explanation:

Antoinette's parents paid at the beginning ($t = 0$) $ 6230, and each year paid annual fees including increases seven times. ($0$) We find that annual fee paid at a given year is represented by the following formula:

$C(t) = C_{o}\cdot \left(1+\frac{r}{100} \right)^{t}$

Where:

$C_{o}$ - Initial annual fees, measured in US dollars.

$C(t)$ - Current annual fees, measured in US dollars.

$r$ - Yearly increase rate, dimensionless.

If we know that $C_{o} = \ \,6230$ and $r =9.5$, first 8 annual fees paid by Antoinette's parents are:

$C(0) = \ \,6230$

$C(1) =\ \,6821.85$

$C(2) = \ \,7469.93$

$C(3) = \ \,8179.57$

$C(4) = \ \,8956.63$

$C(5) = \ \,9807.51$

$C(6) = \ \,10739.22$

$C(7) = \ \,11759.45$

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.

$C_{T} = C(0) +C(1)+C(2) + C(3)+C(4)+C(5)+C(6)+C(7)$

$C_{T} = \ \,6230+\ \,6821.85+\ \,7469.93+\ \,8179.57+\ \,8956.63+\ \,9807.51+\ \,10739.22+\ \,11759.45$

$C_{T} = \ \,69964.16$

Antoinette's parents paid $ 70000 by the time she left the school.