Limitations of Behavioral Finance
The theory of behavioral finance has become exceedingly popular in the past few years. This is largely because of the fact that it mixes the dry, numerical subject of finance with the interesting world of psychology. Most people who read about biases described in behavioral finance books often have a “me too” moment. The biases […]
Government Sponsored Entities
Money market securities are generally issued by firms that have a very strong credit rating. This is because investors do not want their investments to be volatile when they invest in money markets. Hence, they prefer to buy securities only from companies that have a strong credit rating. The government is the most preferable issuer […]
The Sears Bankruptcy
Sears has been one of the largest retailers in the world for many years now. The company has been in operation for about a century. Sears is one of the most widely known corporations in the world. Finally, in October 2018, Sears is now filing bankruptcy. Many investors were already expecting this move given the […]
How Triparty Repo Works?
In the previous article, we have already learned about the repo market. We learned about how the repo market is one of the most important segments of the money market. We also learned about the large volumes of transactions that take place in the repo market. We already know that about $2 trillion to $4 […]
Price Earnings Growth (PEG) Ratio – Formula, Assumptions and Interpretation
The Price Earnings Growth (PEG) Ratio is one of the first variations that were made to the Price to Earnings Ratio to make it more meaningful. The full form of the PEG Ratio is Price Earnings Growth ratio. Instead of being a two way comparison between price and earnings, the PEG ratio makes a three […]
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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