Final answer:
The student's question is about converting an effective annual rate of 12.9% that compounds monthly to an annual percentage rate (APR). To find the APR, use the formula APR = n * ((1 + EAR)^(1/n) - 1), where n is 12 for monthly compounding. The answer will provide the equivalent interest rate that matches the EAR when compounded monthly.
Step-by-step explanation:
The student's question asks about converting an effective annual rate (EAR) into an annual percentage rate (APR) when the interest compounds monthly. To calculate APR from the given EAR, we need to use the following formula:
APR = n * ((1 + EAR)^(1/n) - 1)
Where n is the number of compounding periods per year. When the interest compounds monthly, n is 12. The stated EAR is 12.9%, or 0.129 when expressed as a decimal. Let's perform the calculation:
APR = 12 * ((1 + 0.129)^(1/12) - 1)
Once the APR is calculated, it will provide the equivalent interest rate that, when compounded, would give the same final amount as the EAR of 12.9% over one year. This calculation demonstrates how different compounding frequencies will affect the interest one earns over time. Examples of compound interest provided in Box 1.2 and other instances resonate with the power of starting early investments and how the compound interest can grow an investment significantly over time.