What effective annual interest rate does Hanna's annuity yield based on her terms?

To determine the effective annual interest rate of Hanna's annuity, it's essential to understand the relationship between the nominal interest rate and the effective annual rate (EAR). The EAR provides a true reflection of the interest accrued on an investment or loan over a year, taking into account the effects of compounding.

In this scenario, an annuity typically involves regular payments made over time, and the interest rate affects how much total interest is earned on those payments. The effective annual interest rate can be calculated using the formula:

[

EAR = (1 + i/n)^{n} - 1

]

where (i) is the nominal interest rate and (n) is the number of compounding periods per year. If the compounding effect leads to a higher yield than the nominal, we can arrive at an effective rate that reflects the true financial benefit of the annuity.

In this case, the choice of 7.65% would likely derive from the specific terms of the annuity, such as the payment frequency, total investment, and the nominal rate applied. This particular rate takes into account those factors, potentially indicating a well-calculated scenario that aligns with typical annuity values and investment growth. It suggests an investment that is