I know Ling will be along soon with her nuclear missile truck but...
I thought like you for years but now find it makes huge sense to me on the main car I have. The total of my three year payments for the C5 I've just taken on is less than the first year depreciation from retail and some £6k cheaper over the 3yrs than buying/financing myself! Can't say no to a £6K saving.
I'll admit it has a lower financial advantage on smaller cars which is why we bought our C3 used at 3yrs/23Kmls with cash for the best deal in that sector.
The figures aren't quite as close as you say though. A basic Aygo at £7,800 new discounted will be about £6350 on contract over 3yrs allowing for inclusive VED you would have otherwise paid yourself. I'd not argue that a 3yr old Aygo is worth more than £1500.
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