Using math symbols in openoffice

Sunday, July 25, 2010

In this short article, we will see a short introduction on using math symbols in open office, the motivation comes from the fact that when publishing articles involving math formulae, equations and other functions (like derivatives and integration), its rather convenient to publish them in a form similar to the way we write math functions using the real symbols, this will also improve the readability of those articles which otherwise will be very tedious to interpret when represented with arithmetic operators.

Before publishing articles involving math symbols, one must first know how to use math symbols in openoffice which will be dealt here.

1. Creating math symbols in openoffice, specifying the size of the math symbols
2. Editing math symbols

1. Creating math symbols in openoffice, specifying the size of the math symbols

Lets keep it simple here, we will take a simple compound interest formula, interestingly this comes from my last article involving compound interest, where

FV = P * (1 + r/m) ^ (n * m)

Where

P = Principal (Present value)
r = Interest rate
m = number of compounding periods in an year
n = number of years
FV = Future value (growth)

We need to convert the above expression into the math symbol shown below.

Sample openoffice document with math symbols: math_symbols.odt


Step 1: Type the expression inside the braces, specifying the size, for example if we want to use a medium size for the math formula, then use a size between 3 - 4.

Example: size * 3.2 {Math formula}

For the compound interest formula, this becomes

size * 3.2 { FV = P * (1 + r/m) ^ (n * m) }

Type the above expression in openoffice.

Step 2: Produce the equivalent math symbol

Select the above expression then Insert -> Object -> Formula

Fig 1: Using math symbols in openoffice



As simple as that, your math symbol is ready in two steps.

2. Editing math symbols: After step 2, which generates your math symbol, double click the math symbol box, it would open a text box below where you can edit your math expression.

Fig 2: Editing math symbols in openoffice


Detailed Reference:

1. http://documentation.openoffice.org/manuals/oooauthors2/ (Has several user guides in PDF format, search with math keyword to find the relevant articles related to using math symbols in openoffice).

Investment Science: Yearly, monthly and Continuous compounding

Write it in your head, the formula we learnt in school, the growth in compound interest given by

Where

P = Principal (or Present value)
FV = Growth in compounding (or Future value)
r = Yearly interest rate
m = Number of compounding periods per year (say monthly, quarterly or yearly)
n = number of years (n * m then gives the number of compounding periods for "n" years)

Though this is a simple equation, but the foundations of investment science lies in this simple, yet powerful formula.

For example, if you invest $1000 (P) in a bank for 10 years (n) with an interest rate 5% (r) compounded yearly (m = 1), then the growth in compound interest will be

FV = 1000 * [ (1 + 0.05 / 1) ^ (10 * 1) ] = $1628.89463

That's quite easy, but the fun comes when m > 1 or the number of times the interest compounded per year is > 1, the interest can be compounded every 6 months (m = 2), 3 months (m = 3) or monthly (m = 12).

Assuming that the interest is compounded monthly, then

FV = 1000 * [ (1 + 0.05 / 12) ^ (10 * 12) ] = $1647.0095

The returns in the monthly compounding is little better than that of yearly compounding, in case of continuous compounding, where the number of compounding intervals m -> Infinity, then we have

The below excel spreadsheet (I have used openoffice, but it can be imported as excel) can be used to calculate the compound interest based on the Present value (P), number of years (n), number of compounding intervals (m) and interest rate (r).

1. Compound interest spreadsheet

Question: Try increasing the number of times the interest is compounded yearly (m) in the spreadsheet, note the difference between the growth with that of the growth using continuous compounding.

MS&E242S Investment Science course in Stanford

Thursday, July 22, 2010

You got it right from the above title, I am currently taking the MS&E 242S Investment Science course in Stanford taught by Prof. Charles Feinstien. Although I can tweet about this daily, but I guess a blog about this subject is more appropriate and that's what I am going to do in the coming days, I know the questions you may ask if you are a follower of this blog.

1. Why you didn't blog for sometime?
2. What's in it for me about investment science?
3. What will I learn in the near future about investments?
4. Why are you doing this?
5. Any investment book you recommend?

1. Why you didn't blog for sometime?

Because I believe in writing quality contents compared to quantity and at times when you are busy, its hard to maintain that quality unless you devote sufficient time ane energy for it, again I don't want to give a list of excuses on not blogging for long, but will give enough reasons for why I will be blogging more regularly in future.

2. What's in it for me about investment science?

This is exactly the question which puzzled me before taking the course and the reason why I took this course is just to explore that, to learn the mathematical models and tools used to arrive at major investment decisions.

3. What will I learn in the near future about investments?

Well my plan is not to lecture about investment science, but will educate you about the basics of investment science and financial engineering which everyone should be aware of, like

1. Present Value of an investment
2. Internal rate of return
3. Mortgages, interest, how monthly payments are calculated for your loan if you are paying mortgages
4. Investing in bonds
5. Some reusable excel calculations in investment
6. Exploring the features of a financial calculator to calculate interest, IRR, present values and so on.

Spot rates, forward rates, optimal allocation of your investments, options theory and some practical problems with solutions.

Its highly likely that I will be developing some scripts to illustrate these computations.

4. Why are you doing this?

Its a win-win situation here, I need a definitive reference for these concepts from which you will get benefitted, I took the struggle, Googled, hit the walls to arrive solutions for fundamental problems, a reference for these will make your life easier if you need some introduction fo finance/investment science.

5. Any investment book you recommend?

Old is gold, if you are keen on invesment science, then the reading Investment Science by David G. Luenberger is a must in your bookshelf may you buy bonds, invest in stocks, trade, want to learn about finance or just decided to have some fun with math.

Note: I will be selective in my future blog posts about investment science, some of these concepts may be simple, but yet they are powerful and my goal is to pick a fixed set of concepts which one MUST know about finance and investments.

Ok, lets start the journey today, keep watching.


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