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What happens when we have investments that have different day count bases and compounding frequencies?

In order to compare such investments, we need to convert them to the same day count basis. There are 2 steps:

Step 1:

To convert an interest rate from one compounding basis to another, we must first ensure that both investments are expressed on a bond or money market basis.

Step 2:

When both investments have been converted to the same day count basis, we can then convert them to the same compounding frequency.

Note that the common compounding basis does not have to be equal to the original compounding basis of the investment being compared. For example, one investment might have monthly compounding and another investment annual compounding. Both investments can be converted to a semiannual compounding basis for comparison.

Example

We have 2 investments that we are comparing.

Investment A pays interest of 3% annually, calculated on a bond basis, while Investment B pays interest at 2.95% p.a.