Final answer:
The college student will have $11,520.76 in their savings account after investing $9,000 at a 5% interest rate compounded semiannually for 5 years using the compound interest formula.
Step-by-step explanation:
To find the total amount in the savings account, we need to use the formula for compound interest: A=P(1+r/n)^(nt). In this scenario:
- P is the principal amount ($9,000)
- r is the annual interest rate (5%, or 0.05)
- n is the number of times the interest is compounded per year (2, since it's semiannually)
- t is the number of years the money is invested (5)
Plugging in these numbers we get:
A = 9000(1 + 0.05/2)^(2*5)
A = 9000(1 + 0.025)^(10)
A = 9000(1.025)^10
A = 9000(1.280084)
A = $11,520.76
Therefore, the college student will have $11,520.76 in their savings account after 5 years.