Average UK Student Debt - Dodgy Numbers?

It's being widely reported this morning that average UK student debt could reach £53,000 for students starting when the new fees kick in. Example here from the BBC. The figures come from some organisation called Push. The relevant page is here.

The only problem is that I cannot work out how their numbers are derived. Each year they take a survey of student debt across the UK. That's fine. This year they found that the average debt for the UK was £5,681, an increase of 6.4% on last year. They're projecting that average debt will be £6,043 next year, an increase of about 6.4% again.

However, for those starting in 2012 the average debt in their first year is predicted to be £15,581 assuming tuition fees of £8,630. If we deduct the fees then projected debt is £6,951. If we deduct the fees from their projections of those starting this year (ie £6,043 - £3,290) we get £2,753. So that means that not only will fees rise by about 2.5 times but also all other expenses will increase by the same amount. That doesn't seem right to me.

I've emailed the organisation for an explanation and will see what comes.

UPDATE: Johnny Rich from Push emailed me the following:

We don't say the first yr debt in 2012 is £15,581. We haven't calculated that figure. The discrepancy that's troubling you may arise from the fact that the £53k number stretches over an average course of 3.43 years (the average in our survey) and we projected compound increases in living costs over the same period. 

On the first point I appear to have made a mistake. The £15,581 is not debt in the first year but average debt over the 3.43 year course. However, I'm still very confused. Partly this is because the £26,100 debt accrued by someone starting this year must be spread over 4.3 years to give an average of £6,403. But I'm also now confused as to how the figures are arrived at.

The logical way to do this, as far as I can see, is to work out the average debt per year and then sum them. Average the result if needed. Assuming a constant rate of increase of 6.4% per year (which is not a safe assumption in itself in any case) we would not get £53,000 for a 3.43 year course. Instead we'd get something like £44,000.

I'm very surprised that they haven't calculated the figure for the average debt in 2012/13. How did they generate their results?

It's all a little unclear and Push should really publish the details of their methodology. I notice also that I'm not the only person doubting the figures. Wes Streeting, former NUS President, also doubts them on his twitter feed.