October 13th, 2009
It is said that we are in a recession when your neighbor is unemployed but we are in a depression when you are unemployed.
Where are we and where are we going economically?
The real Gross Domestic Product (GDP) declined by 6.4% in the first quarter of 2009 and by 1.0% in the second quarter. This was largely the result of reduced consumer spending and declines in investments, inventories and construction. Government spending increased during this period.
After declining in 2008 corporate profits increased by 5% in the first quarter of 2009 and by 5.7% in the second quarter. Financial corporate profit grew by 16.7% in the second quarter.
Imports decreased during the first two quarters of 2009. The net deficit on international trade decreased in both the first and second quarters. Total personal income in Boston increased by 6.4% in 2007 but by only 3.7% in 2008 because of the ongoing economic recession. Personal income for the US as a whole increased by 6.0% in 2007 and by 3.4% in 2008. Thus Boston appears to be doing better than the rest of the country but not by much. In terms of per capita income Boston ranked 9th in the nation. Bridgeport/Stamford-Norwalk CT came in first.
The outlook is for increased growth in the economy accompanied by a more sluggish labor market. Below are some of the expectations for the next several years.
The long run outlook for the period 2009 to 2018 is that the CPI will increase at an annual rate of 2.50% and the index for PCE will increase at an annual rate of 2.15%.
Overall expectations are for a constant but lower rate of growth over the next several years. The major area of concern will be unemployment/job creation.
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October 1st, 2009
Effective Annual Rates of Return and Present Values
I just finished teaching a finance course to graduate students in an MBA program. Two of the subjects covered in this course were rates of return and present value. The students were able to handle the calculations but were unaware of some of the concepts.
What happens when you compound interest rates? Does the effective rate rise as the number of times that the rate is compounded increases? I am sure you all remember the offers by many banks. “Deposit with us and you will get a free toaster and interest will be compounded continuously.” There is a general belief that the more times that the interest is compounded, the higher the annual rate. This is an erroneous concept. As the number of times the interest is compounded the effective annual rate increase but there is an upper limit.
If the interest is 6% and it is compounded twice a year the effective annual rate is 6.09%. If it is compounded 12 times per year the effective annual rate is 6.168%. Compounding it 24 times per year results in an annual rate of 6.170% and compounding it 100 times per year results in an annual rate of 6.181%.
Note how the effective annual rate increases as the number of times it is compounded increases but the size of the increase becomes smaller and smaller. In fact, if you compounded 6% an infinite number of times in a year, the annual rate would be 6.184%. This is the maximum annual rate. Note how close this figure is to the effective rate for compounding 24 times per year.
If the annual interest rate was 12%, compounding it 4 times per year would result in an effective annual rate of 12.551%. However, compounding it 100 times per year results in an annual rate of 12.742% and compounding it an infinite number of times per year results in an annual rate of 12.750%; not much greater than the result from compounding it 24 times per year. The table below shows the effective annual rate for the nominal interest rates between 5% and 18% based upon an increased number of compounding periods. As can be seen, the increase due to compounding becomes very small as the number of compounding periods increases. This is a concept that is not always understood and thus it is often used to infer that increased compounding will yield greater rates of returns.
Tags: annual rates of return, interest rate, mba, profit
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