Add-On Rate, Actual/365
Many money markets use actual/365 for the fraction of the year, in particular those markets that have followed British conventions. The add-on rates for 2015 and 2016 are:
In some markets, the number of days in the year switches to 366 for leap years. This day-count convention is known as actual/actual instead of actual/365. The interest rate would be a little higher.
Add-On Rate, 30/360
An easier way of counting the number of days between dates is to use the 30/360 day-count convention. Rather than work with an actual calendar (or use a computer), we simply assume that each month has 30 days. Therefore, there are assumed to be 30 days from January 12 to February 12 and another 30 days between February 12 and March 12. That makes 60 days for the time period and 360 days for the year. We get the same rate for both 2015 and 2016:
This day-count convention is rare in money markets but commonly is used for calculating the accrued interest on fixed-income bonds.
Add-On Rate, Actual/370
Okay, actual/370 does not really exist – but it could. After all, 370 days represents on average a year more accurately than does 360 days. Importantly, the calculated interest rate to the investor goes up. Assume 59 days in the time period.
Think of the marketing possibilities for a commercial bank that uses 370 days in the year for quoting its deposit rates: “We give you five extra days in the year to earn interest!” The cash flows have not changed. The future cash flow (the FV) is the initial amount (the PV) multiplied by one plus the annual interest rate times the fraction of the year. For the same cash flows and number of days in the time period, raising the assumed number of days in the year lowers the fraction and “allows” the quoted annual interest rate to be higher. Why hasn't a bank thought of this?
Discount Rate, Actual/360
Discount rates by design always understate the investor's rate of return and the borrower's cost of funds. Assume again that the year is 2015.
Note that this discount rate can be restated as an equivalent 360-day add-on rate using the conversion equation 1.8, matching the earlier result.
It is critically important to know the rate quotation and day-count convention when working with money market interest rates. This example demonstrates that many different money market interest rates can be used to summarize the two cash flows on the transaction. It is also important to know when one rate needs to be converted for comparison to another. For example, to convert a money market rate quoted on an actual/360 add-on basis to a full-year or 365-day basis, simply multiply by 365/360. However, a rate quoted on a 30/360 basis already is stated for a full year. It is a mistake to gross it up by multiplying by 365/360.