Many thanks for this incredible material.
I've got a doubt regarding the calculation of the quarterly interest. I thought that the conversion from annual interest to a smaller period interest shouldn't be just a division. I thought that you should always consider the time value of money. Therefore the calculation would be:
((annual interest + 1 ) ^ ( # days/ days in a year) )- 1
Is my understanding correct?
This is a great question and an area of common misunderstanding.
The calculation we use to convert an annual interest rate to a period interest rate depends on:
- How the annual interest rate has been expressed and whether the interest is being rolled up into the debt balance
- The day count convention used to define what a year is for interest purposes.
How the rate has been expressed.
The rate has been expressed as an effective interest rate. To convert from an effective interest rate to a period rate, you would decompound it using the calculation you mention in your question.
Let's ignore day count conventions for the moment. If you had an effective annual rate of 6%, being compounded in four equal quarterly amounts, the amount of interest that would be charged each quarter would be per your formula:
Where Rp is the period rate and Ra is the annual rate:
Rp = (1 + Ra) ^ (1 / 4) - 1
The rate has been expressed as a nominal rate. If this is the case then we do not decompound to calculate the period rate. This is the case that you are seeing in the case study model.
In this case, the interest is being paid quarterly and is not compounding or rolling up into the debt balance.
In this case, again assuming equal quarters, the amount of interest would be given by:
Rp = Ra / 4
However, we also have to take into account the day count convention being used to express the interest rate.
Day count convention
There are different day count conventions for different financial products in different markets. You'll see these expressed as, for example, act/360 or act/365. When calculating the period rate, it's important to be sure of the day count convention being used to express the annual rate. With an act/360-day count convention, you would use 360 as the "days in year" for the conversion.
To calculate a period rate from an annual nominal act/360 rate:
Rp = Ra / 360 * DaysInPeriod
To calculate a period rate from an annual effective act/360 rate:
Rp = (1 + Ra) ^ (DaysInPeriod / 360) - 1
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