So you’ve reached that bit of the Number curriculum at the end of Percentages – Simple and Compound interest. The theory is straight forward enough:
- Simple interest is calculated on the original balance.
- Compound interest is calculated fresh every year on the current balance.
This shouldn’t be a tricky concept, yet it is frequently glossed over or partially taught to lower ability students. This is the maths they’ll need to get their head around at the bank in a few years time. So why not replace the scary calculations and rote learning with diagrams, which embed understanding.
- Coloured pens
- Squared paper
- Calculator (Optional)
Simple Interest: Step 1
Draw a square which has sides which are a multiple of ten (I used 10×10). This area represents the original investment.
Assume the interest rate is 10%. Calculate 10% of the area and shade it in lightly. Basically one column, since it’s a 10×10 grid.
Add on 10% by drawing the shaded area again. This is the 1st interest payment.
Repeat Step 3 for the 2nd and 3rd years.
In summary, a simple interest (10%) investment over 3 years is the same as adding on 30%.
Compound Interest: Step 1
Repeat steps 1 -3 of simple interest
Work out 10% of the height and draw a new row – since the grid is 10 squares high, it’s simply one square high.
Notice that the row is wider than the original square – the dotted area indicates the extra interest earned on the previous years interest. This starts the discussion that you are not adding on the same amount each time.
Using the same concept as Step 2, work out 10% of the width of the diagram. This time the width is a little more than one square wide.
Once again it’s clear to see that you are adding on more than the last year.
Comparison: Simple vs Compound interest
Which is the better investment? It’s pretty clear to see:
You can compare these two types of interest using area calculations, rather than long lists of percentage calculations and you can actually ‘see’ the different methods.