Final answer:
The balance of $500 invested at an 8% interest rate compounded quarterly cannot be determined exactly without knowing the number of years. If, for example, we assume the money is invested for 3 years, the formula yields a balance of $634.12, not matching any of the provided options.
Step-by-step explanation:
To calculate the balance after a certain period with compound interest, we use the compound interest formula:
A = P(1 + r/n)^(nt), where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
In this particular case, an initial investment of $500 at an 8% annual interest rate, compounded quarterly, means we use n = 4 (since interest is compounded quarterly). However, we're missing the number of years (t) the money is invested from the question provided. If, for example, the investment was for 3 years (which we'll assume for our calculations), the balance can be calculated as follows:
A = 500(1 + 0.08/4)^(4*3)
A = 500(1 + 0.02)^12
A = 500(1.02)^12
A = 500 * 1.26824
A = $634.12
Without the number of years specified, we cannot determine the exact balance, and thus none of the options provided would be correct. As for the reference to a total of $115.76, this seems to be based on a different principal amount and might not be directly relevant to the question at hand.