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:
\[ \boxed{115,224.04} \]