I am reading and working through the book ‘Mathematics for Economics and Finance’ at the moment by Martin Anthony and Norman Biggs.
I am learning the mathematics that is detailed in the trading course ‘Certificate in Quantitive Finance’ to prepare myself both for working in finance and building my trading platform.
At the moment I have just learnt about First order linear recurrence equations and how this relates to working out capital gained on compound interest in an account with a constant percentage rate.
I have always worked this out before in Excel with arduous calculations for each year, now I have the maths to do it for any year in one calculation. It is quite a buzz to see the power of mathematics at work in real life.
Why didn’t they make it this interesting at school!
Standard First order linear recurrence for compound interest can be expressed in maths as:
yt = ayt-1 + b
where y is the capital at year t, a is (1 + r) where r is the interest rate as a decimal, and b is zero.
This gives
yt = (1 + r)ty0
or Capital after t years = (1 + r) to the power of t multiplied by the initial capital.
If the equation is reversed, then we can see how much we need in the bank to achieve a target t years in the future.
y0 = yt / (1 + r)t
or
capital needed is the desired target amount divided by (1 + the interest rate) to the power of the number of years.
Easy as pie!