"I have an annuity but I need cash now."

[Johnh]

A few years ago I took the opportunity to make a deal like this. I was 55 I had paid for a few years into a company pension fund in the UK, finishing about 15 years before. A full career paid into this system would have given me an annual pension of about 2/3 of final salary, which was the traditional way these pensions worked. After just a few years paying in, it would have given me just a few thousand a year after age 65 Not insignificant but not enough to make big plans around.

So after checking out some offers, I sold it for a lump sum that was about 50x the expected annual payment, and invested it in a fund to use later. I can draw on it at any time, but uk pensions are taxable so I'll wait until I stop earning elsewhere

At the time, interest rates were historically low, and these types of pensions were being phased out. I was told that to provide that company pension would have been very expensive for the company, since it is effectively an annuity and to cover that annual commitment in an environment of low interest would have meant paying a huge amount for the annuity, hence the company was willing to pay a high sum to get out of this liability. The arrangement puts me much better in control too, and anything left will remain in my estate after I've gone.

So this situation seems to fit in with the topic of this thread. So, how would the maths work?