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

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

Explanation:

Antoinette's parents paid at the beginning (
`t = 0`) $ 6230, and each year paid annual fees including increases seven times. (
`0 <t \leq 7`) We find that annual fee paid at a given year is represented by the following formula:

`C(t) = C_(o)\cdot \left(1+(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.