6690 - Using Computers in Mathematics Instruction
Danie Brink
Essay 1: Financial Mathematics
Let me start off this essay with the following scenario. Hopefully it will fancy your interest to read the rest of the page.
Two friends invest money for their retirement. Friend 1 invests $1000 per year at 6% interest compounded yearly. After ten years, friend 1 stops investing the $1000 per year but invests just the amount he has saved up during the past ten years at 6% per annum compounded yearly for the next 26 years. Friend 2 realizes that he has to start investing also. He invests $1000 per annum for the next 26 years at 6% per annum compounded yearly. At the end of the 36 years, who has more money? Click here to see the answer.
According to Albert Einstein, to understand the power of compound interest is to understand the most powerful and important formula in the world. To use the concept of compound interest to your advantage will make someone with a moderate salary financially independent and debt-free over time, while to be ignorant of the concept of compound interest can make someone with an above average salary live in debt and poverty forever. In this write-up we are going to explore the concepts of personal finances, interest rates, loans and investments and hopefully get to understand this powerful phenomenon called compound interest. Hopefully we will be able to apply it to our daily lives.
In our explorations, we will make use of the following software:
1. Microsoft Excell
2. Microsoft Word
3. Geometer's Sketchpad version 4.06
4. Graphing Calculator version 3.2.
Firstly, we are going to derive some very important formulae which are essential to do significant financial mathematics. The three important formulae that we will derive for the purposes of this website are:
a) The investment formula - this is the formula that we will use to determine the value of a single investment over a given period of time.
— Here are some examples of investment problems.
b) The annuity formula - this is the formula that we will use to determine the value of an annuity (typically a monthly investment) over a given period of time.
— Here are some examples of annuity problems.
c) The mortgage formula - this is the formula that we will use to determine the payment (typically monthly) on a mortgage.
— Here are some examples of mortgage problems.
Secondly we are going to see if we can discover why Albert Einstein called compound interest the most important formula in mathematics by making use of technology. In order for us to vividly see some results, we will do this with the help of some technology.
i) The first illustration is an Excel spreadsheet that shows the difference in growth of an investment made at 6% per annum versus an investment made at 8% per annum.
ii) The next illustration is another Excel spreadsheet that will show you the difference over a 20 year period of an investment of $100, $120 and $140 per month. If this result does not show you the power of compound interest, nothing will.
iii) The last illustration is another Excel spreadsheet that will show you the difference in bond repayments when the interest rate fluctuate between 1% and 25%. If you wonder about the 25% bond interest rate, you obviously do not come from a Third World country.
Lastly, we will wrap up the essay with some conclusions that will make us financially independent and debt free.
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Link to my 6690 Main Page