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.
$

1 answer

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:

\[ \boxed{115,224.04} \]