When determining the effective interest rate, what impact does semiannual compounding have?

When assessing the impact of semiannual compounding on the effective interest rate, it is essential to understand how compounding frequency affects the overall interest that accumulates on an investment or loan.

When interest is compounded more frequently than annually, the effective interest rate increases compared to the nominal rate. This is due to the fact that with semiannual compounding, interest is calculated and added to the principal twice a year. As a result, each time interest is applied, it is based on a principal amount that has already increased from earlier interest accumulations, leading to a phenomenon known as "interest on interest."

With semiannual compounding, the effective annual rate can be calculated using the formula:

[ \text{Effective Rate} = \left(1 + \frac{r}{n}\right)^{n} - 1 ]

where ( r ) is the nominal interest rate, and ( n ) is the number of compounding periods per year. For semiannual compounding, ( n ) would be 2. This calculation will yield an effective interest rate higher than the nominal interest rate due to this more frequent compounding effect.

This principle illustrates why semiannual compounding indeed increases the effective interest rate,