Thursday, 3 January 2013

Compound interest

A friend runs a company undertaking facilities management contracts for offices here in London. Contracts tend to be from three to six years in length and have price indexing built-in, normally by reference to an index or combination of indices published by the ONS. In every case, she says, it is this indexing that provides the profit margin. Typically in year one the contract breaks-even or racks up a slight loss and by year three is comfortably in profit. All she has to do is keep costs within the indices - a process of good management and fine tuning.

In the days when school maths involved the calculation of compound interest any schoolboy would have understood the relationship. These days it takes the IFS to explain the effects of using different indices to uprate benefits. 

Labour used the RPI or a variant of the Rossi index to calculate benefit increases; although this was changed by the current government to the CPI, and subsequently to a cap of 1% for the next increase, the increase last year of 5% and previous increases based on RPI have taken the welfare bill to £208bn - a third of public expenditure. The effect of compounding is easily demonstrated by the following example; 


Inflate £ millions Inflate £ millions
Year 0
180,000
180,000
Year 1 3.10% 185,580 1.00% 181,800
Year 2 2.80% 190,776 1.00% 183,618
Year 3 3.70% 197,835 1.00% 185,454
Year 4 5.00% 207,727 1.00% 187,309
Total increase
27,727
7,309

The difference between the two, of about £20 billion, is equal to half the UK defence budget. Last year's 5% increase alone outweighed all the cuts made by IFS to disability benefits.

7 comments:

Anonymous said...

Yep and a 1% cap is in effect a decrease in the benefit rate, when RPI inflation is factored in. Actually, the other reality, inflation for people living on benefits and the those on a basic pension will be much higher than the RPI [food and heating] - so they'll be losing out big style but: it has to be done.....doesn't it?

Blue Eyes said...

"Welfare" might well be a third of public spending but pensions is the biggie and Cameron has made a promise to pensioners. However a low cap on rises is better than Labour's policy of increasing benefits so fast that people notice the poor having a higher standard of living than the middle class.

Lee said...

JSA paid to people who are unemployed amounts to less than half the foreign aid budget. Most benefits are paid to people in work, disabled or retired.

Demetrius said...

We seem now to have a couple of generations the great majority of whom simply do not know what compound interest is and therefore the implications. It may account for the severe money problems many have and the disasters to come.

Anonymous said...

Many do know, and were educated so. Many more do not, and were similarly educated so. Hence payday loans where even a figure of over 3000% seems to not be a restriction.
As to CPI/RPI....the basic state pension is not affected, nor is pension credit. CPI starts at the second state pension. Funnily enough that means that public service pensions will also be calculated using CPI. And some private pensions will also be affected. We'll have to wait on that for the changes to the various pension laws...
The other minor problem is that RPI is calculated arithmetically, while CPI is calculated geometrically.....there is a rather nice graph on the touchstone blog about it....

http://touchstoneblog.org.uk/2010/06/the-difference-between-an-arithmetic-mean-and-a-geometric-mean-and-why-it-matters/

Compound interest works both ways...

Raedwald said...

Anon 1 - my gross pay is now exactly what it was 4 years ago; 1% a year would be fantastic. Much of the construction sector has had pay frozen since 2008.

Anonymous said...

My pay is now 15% less than 5 years ago....but that still leaves me much better-off than a person on the basic state pension. 1% of 80 quid isn't going to break the bank. Even our already broken living-off-state-benefits banks....
So exactly how much state benefits did our corrupt banks deprive us of....didn't I hear numbers up near the trillion-pound figure ?
Much of which departed to foreign climes, while the tax relief was claimed for their losses...and they still are not lending...
So if we're looking for benefit cheats....we should wander along to the high street bank and look inside..