Question

A private high school charges $53,797 for tuition, but this figure is expected to rise 10% per year. What will tuition be in 8 years?
If necessary, round your answer to the nearest cent.
$

Answer 1

To calculate the tuition after 8 years with an annual increase of 10%, we can use the formula for compound interest, which is:

\[
A = P(1 + r)^n
\]

where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of years the money is invested or borrowed.

In this case:
- \( P = 53,797 \) (the initial tuition)
- \( r = 0.10 \) (10% increase)
- \( n = 8 \) (number of years)

Now, we can substitute these values into the formula:

\[
A = 53,797(1 + 0.10)^8
\]

Calculating \( (1 + 0.10)^8 \):

\[
(1.10)^8 \approx 2.1436
\]

Now, multiply this by the initial tuition:

\[
A \approx 53,797 \times 2.1436 \approx 115,224.04
\]

Thus, the tuition in 8 years will be approximately:

\[
\boxed{115,224.04}
\]