## Thursday, July 04, 2013

### An interest in interest

Today, I noticed two adverts. One for some form of card with an APR of 627%, one for a current account with around 2.5% interest. The problem with these adverts is that many people neither realise how percentages work nor the impact of compound interest. Hence, I prefer a simpler way of expressing this in an easy to understand language.

What I'd like to see is the adverts shout out the impact of either saving or borrowing £100 under these terms for five years. However, the problem with this is the impact of tax, any charges and the issue of inflation i.e. tomorrow's pound may buy more than today's but it is more likely to buy less than today's and hence you have to adjust for this. Even if you decide to deal with inflation then which inflation figures? We have a tendency of changing the basket of goods we measure on. However let us assume we take CPI as the inflation measure, let us also assume for simplicity of this example that the figure is 5%.

So in the case of saving my £100 would become :-
£100 * (1 + 0.025)^5 / (1.05)^5 = 100 * 1.13 / 1.28 = £88.

Of course, the actual amount you get back will be higher but its spending power due to inflation is lower hence we will reflect this in real terms of today's money. So my current account advert rather than saying 2.5% interest could simply state "Save £100 with us and we will give you back £88 in five years time (minus any tax)"

For my loan of £100 then the amount to be repaid would be
£100 * (1 + 6.27)^5 / (1.05)^5 = 100 * 20,308 / 1.28 = £1,586,580

Hence my credit card advert rather than saying 627% APR could simply state
"Borrow £100 from us and pay back £1,586,580 in five years time (plus any charges)"

Now these are figures people can understand. Obviously the loan industry will be trying to get reported CPI figures to be shown as higher (so the cost is lower) and the saving industry will be trying to get CPI figures shown as lower (so the return is higher). However that sort of tension is always good if you want to get something closer to the truth.

So, I thought I'd create my own updated adverts. Ok, they're not so jazzy as the real thing but I did add kittens for a bit of cuteness and some action statements - spend and save. I also think the message is a bit clearer.