Terman’s law: “Education is what you get from reading the small print.  Experience is what you get from not reading it”

PART 1 – The Theory

Please don’t be frightened off this initial part as possibly being too technical - it is not as mathematical as you think.  It is important to understand the shape and feel of the figures illustrated in the various tables.  It is not necessary to test every line, unless you are a real enthusiast.  I have included the more technical bits in a separate section at the end of Part I, so it’s all there if you wish to indulge in the full magic of the maths, and of course the figures reappear in the spreadsheets together with the formulae used.

Simple and Compound interest - the fundamentals  
Banking may not be the oldest profession but it was probably started by demand from the oldest profession.  There are people who have money and those who need it.  Depositors or investors want a safe return on their capital, and businessmen and others want to raise capital for a variety of reasons.  The bank was the earliest go-between, passing back to their depositors most of the interest they charge their borrowers, naturally retaining a modest margin for themselves.  Building Societies were formed later on as mutual non-profit making businesses to focus on straightforward savings and the provision of mortgages.

These Institutions created the need for some basic mathematics to enable them to maintain a fair and consistent standard for rewarding investors and charging borrowers.  They had to have some simple formulae to calculate interest over time.  The phrase Time is Money is an exact science as far as banks are concerned, as time is the essential ingredient of interest. 

You were probably taught that there are two ways of calculating interest, simple, and the more prevalent compound interest.  Simple interest is really just a simple way of calculating interest. The method used to calculate it is actually quite inaccurate but it was fashionable before computers enabled more complex but more exact calculations to be performed.  The use of simple interest as a measuring tool is quite ineffective in most cases and certainly is of no value for comparing today’s sophisticated financial products. 

Compound interest is the only mathematically correct method for measuring and comparing loan products.  It is undoubtedly more fascinating but it demands more than a superficial understanding and it does require more thoughtful mathematical processes.

Simple interest ignores capitalised interest
If you borrow £1,000 at 12% per annum simple interest without paying back any capital, the interest is £120 at the end of each and every year - twelve hundredths of the capital invested.  Simple interest ignores the fact that interest can itself attract interest.  See Figure 1 for an easy illustration.

I have used the term principal to identify the initial cash that starts any financial transaction.  £1,000 is the principle in this example.  Whilst this is probably an old-fashioned word, it distinguishes itself from future capital within any transaction sequence, which thereafter is simply referred to as Capital.  These days you will more often hear the words present value instead of principal and future value as future capital.