"You can choose to top up your State Pension by between £1 and £25 per week. How much you’ll need to contribute depends on:
how much extra pension you want to get each week
how old you are when you make the contribution
Example
You are 68 years old in October 2015. You decide that you want to get an extra £5 per week (£260 a year) on top of your pension.
The cost of an extra £1 per week for a 68 year old is £827, so you multiply £827 by 5.
You’ll make a lump sum payment of £4,135."
So if you are 68 years old, you have to gamble on living at least 16 more years, until you are 84 to make your investment back.
Yet, according to the Office for National Statistics, average life expectancy for men is 79.2 years (76.6 in Scotland) and for women 83.0 years (80.8 in Scotland).
They don't mention that on the pension top-up website...