What is the effective interest rate for a mortgage that compounds semi-annually?

To determine the effective interest rate for a mortgage that compounds semi-annually, it's essential to understand how compounding works and how it affects the nominal interest rate.

When interest is compounded semi-annually, it means that the interest is calculated and added to the principal every six months. This compounding frequency can lead to an effective interest rate that is higher than the nominal rate due to the effects of interest being earned on previously accrued interest.

To convert a nominal annual interest rate to an effective annual rate when compounding occurs more than once per year, you can use the formula:

[

\text{Effective Interest Rate} = \left(1 + \frac{r}{m}\right)^{m} - 1

]

In this formula, ( r ) is the nominal annual interest rate expressed as a decimal, and ( m ) is the number of compounding periods per year (for semi-annual compounding, ( m = 2 )).

For choice C, if we were to assume a nominal interest rate of 5.70%:

1. Convert the interest rate to decimal form: 5.70% = 0.057.

2. Apply the compounding formula:

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