Final answer:
The effective annual interest rate for an APR of 8% compounded monthly is approximately 8.30%. This is calculated using the formula for compound interest, illustrating how compounding can enhance returns or costs.
Step-by-step explanation:
The student's question pertains to finding the effective annual interest rate given an annual percentage rate (APR) of 8%, compounded monthly. To calculate the effective annual interest rate (EAR), we use the formula EAR = (1 + APR/n)^n - 1, where APR is the annual percentage rate and n is the number of compounding periods per year.
In this case, since the APR is 8% or 0.08 as a decimal, and there are 12 compounding periods per year (monthly compounding), the calculation would be:
EAR = (1 + 0.08/12)^12 - 1
When we solve this calculation, we determine the EAR to be approximately 8.30%, which means the actual interest earned over a year is higher than the nominal APR of 8%.
This example illustrates that compound interest can significantly impact the growth of an investment or the cost of a loan. In essence, with each compounding period, interest is earned on the previous interest, leading to potentially higher returns or costs than one would expect with simple interest.