Final answer:
The company will have $14,323.64 in 8 years after investing $10,000 at a 4.5% annual interest rate compounded quarterly.
Step-by-step explanation:
To answer the question, first, we need to use the formula for compound interest which is A = P(1 + r/n)nt, 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 times that interest is compounded per year.
t is the time the money is invested for, in years.
In this scenario, the company owner invests $10,000 at an interest rate of 4.5% compounded quarterly for 8 years. Inserting these values into the formula gives us:
P = $10,000, r = 4.5/100 = 0.045, n = 4, t = 8
Therefore:
A = $10,000(1 + 0.045/4)4*8
Calculating this, we get:
A = $10,000(1 + 0.01125)32
A = $10,000(1.01125)32
A = $10,000 * 1.432364
A = $14,323.64 (rounded to two decimal places)
Thus, the company will have $14,323.64 available in 8 years.