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It is common knowledge that investment bankers help a company when they want to list their shares on the stock exchange. This process is called listing, and there are hundreds of companies that undertake this process every year. However, the opposite of this process also happens. This means that companies that are already publicly listed […]
Income Approach to Valuation of Sports Franchises
From the previous articles, we now know that sports franchises across the world are now being viewed as commercial entities. Hence, it is vital to derive the correct valuation for them in order to ensure that buy and sell as well as restructuring transactions can take place at the correct valuation. However, we also know […]
Commercial Paper: A Primer
In the previous articles, we have discussed that the money market has various sub-sections. One of the most important sub-markets is the commercial paper market. The commercial paper market accounts for a sizeable amount of funds that flow through the money market. In this article, we will have a closer look at the details of […]
The Decline of the Big Corporation
The era of big corporations started during the industrial revolution. The past couple of centuries have witnessed the rise of these mega-corporations, particularly in the developed western world. In many cases, these corporations have become extremely powerful and have behaved aggressively with weaker nation-states as well. The idea that some private individuals can amass more […]
How Money Market Impacts Other Markets?
In the previous articles, we have learned that the money market is a very important market in our financial system. However, it is also important to note that the money market can have an impact on almost all other financial markets. Central banks all over the world try to control the monetary policy of their […]
Theoretically there are two types of interest rates, simple and compounding. However, in finance the word interest usually refers to compound interest. Simple interest almost never factors in financial calculations. In all calculations related to present values and future values, compound interest is used. However, as a student of corporate finance, it is essential to know the difference that compounding intervals have on the effective interest rate that is paid on the investment. This article explains the same:
We are all aware of the difference between simple and compound interest. However, just to reiterate, the principal amount never changes in a simple interest calculation. So if $100 are lent for 3 years at 10% simple interest, the interest paid in each of the 3 years would be $10.
But if $100 were lent at 10% for 3 years and compounding happens annually, the interest payments would be $10, $11 and $13.1 for years 1,2 and 3 respectively. This is because at the end of each period the accrued interest gets added to the principal and therefore the interest in the next period is a little bit more.
In case of compound interest 10% compounded annually and 10% compounded semi-annually i.e. twice a year do not means the same thing. Let’s understand this with the help of an example:
Annual Compounding: $100 @10%, Interest = $10
Semi-Annual Compounding: $100 @10%, Interest $5 after 6 months and %5.25 after another 6 months. Hence the total interest would be $10.25 as opposed to $10 on an annual basis.
Rates Increase As Compounding Intervals Grow Smaller:
As we can see from the above example that semi-annual rates give more interest than the annual rates. We can extend this logic further and say that monthly rates will provide more interest as compared to semi-annual rates and weekly rates will provide more interest than monthly rates.
As a thumb rule, we can say that the smaller the compounding intervals, the higher the interest rates will be. As far as investments are concerned, most rates are compounded annually or semi-annually. Smaller compounding frequencies are not used. In common usage, only in the case of credit cards are the rates expressed as monthly compounding interest rates.
Until now, we have considered discrete intervals at which interest was being paid. We could bring the intervals down to hours, minutes or even seconds and yet they will be discrete. Theoretically it is possible that interest be paid continuously over a given period of time. This is not possible in reality. However, continuously compounded interest rates provide some ease in mathematical calculations. It is for this reason that they are often used in finance. Compounded interest rates can be converted into continuously compounded interest rates by multiplying them with — ert
Where:
e = 2.718
r = annually compounded rate of interest
t = number of time periods
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