What is the effective annual rate on Emma's annuity, based on her monthly payments?

The effective annual rate (EAR) is a key metric used to determine the actual return on an investment or the effective cost of a loan when compounding occurs more frequently than once a year. To calculate the EAR from an annuity based on monthly payments, you typically first need to identify the nominal annual interest rate and the frequency of compounding.

In Emma's case, if her monthly payments are producing an effective annual rate of 5.30%, this suggests that when her payments are factored in with the monthly compounding periods, the result effectively translates into an annual yield of 5.30% when compounded monthly.

The calculation of the effective annual rate involves the formula:

[ EAR = (1 + \frac{i}{n})^{n} - 1 ]

Where:

• i is the nominal interest rate (annual rate).

• n is the number of compounding periods per year (12 for monthly).

If the interest rate were, for instance, aligned with compounding monthly, the conversion indicates she realized this effective annual yield through her structured payment plan.

This calculation is crucial for understanding how much interest she effectively earns or pays in terms of annualized returns from her annuity, making 5.30% the appropriate answer