TWO CASH FLOWS, MANY MONEY MARKET RATES

Suppose that a money market security can be purchased on January 12 for $64,000. The security matures on March 12, paying $65,000. To review the money market calculations seen so far, let's calculate the interest rate on the security to the nearest one-tenth of a basis point, given the following quotation methods and day-count conventions:

■ Add-on Rate, Actual/360

■ Add-on Rate, Actual/365

■ Add-on Rate, 30/360

■ Add-on Rate, Actual/370

■ Discount Rate, Actual/360

Note first that interest rate calculations are invariant to scale. That means you will get the same answers if you simply use $64 and $65 for the two cash flows. However, if you work for a major financial institution and are used to dealing with large transactions, you can work with $64 million and $65 million to make the exercise seem more relevant. Interest rate calculations are also invariant to currency. These could be U.S. or Canadian dollars. If you prefer, you can designate the currencies to be the euro, British pound sterling, Japanese yen, Swedish krona, Korean won, Mexican peso, or South African rand.

Add-On Rate, Actual/360

Actual/360 means that the fraction of the year is the actual number of days between settlement and maturity divided by 360. There are actually 59 days between January 12 and March 12 in non-leap years and 60 days during a leap year. A key word here is “between.” The relevant time period in most financial markets is based on the number of days between the starting and ending dates. In other words, “parking lot rules” (whereby both the starting and ending dates count) do not apply.

Assume we are doing the calculation for 2015.

Note that the periodicity for this add-on rate is 360/59, the reciprocal of the fraction of the year. If we do the calculation for 2016, the rate is a bit lower.