One of the main things to remember about short-term investing and borrowing equations is that whether you’re calculating the interest earned on a short-term investment or the interest expense of a short-term borrowing arrangement, these equations are all a variation of the same underlying theme which is:
Interest (i.e. what you earn or what you pay) = Rate x Amount x Time
That is, some amount of money is either invested or borrowed at some interest rate for some period of time. An easy way to remember this is that it spells RAT.
It follows then, that the investment yield and borrowing cost equations are also a variation of RAT. In this case however, you’re solving for the “Rate” which looks like this:
Rate (i.e. investment yield or borrowing cost) = (Interest / Amount) x Time
Here’s a tip regarding the “Time” variable in RAT. The “Time” variable represents either the holding period of an investment or the period that funds are borrowed and these numbers of days are related to a either a 360 day or a 365 day year depending on the requirements of the calculation. Frequently, the question has comes up concerning how to remember if the days of the year is placed in the numerator or in the denominator of the “Time” variable for a given calculation. These rules might help:
1. If the result of the calculation is expressed in dollars, then the days in the year are placed in the denominator. For example:
Dollar Discount = Discount Rate x Par Value x Days / 360
= R x A x T
2. If the result of the calculation is expressed as a percentage, then the days in the year are placed in the numerator. For example:
Discount Rate = Dollar Discount / Par Value x 360 / Days
R = A T
So, looking for the underlying theme of “RAT” as you study these equations might help you to recall the one you need to answer a calculation question on the exam.
- George Schilling, CTP