Annuities, a note on price theory

While researching my articles on the UK 2014 budget, I wanted to write a quick note on Annuity prices, yields and interest rates, I came across nothing easy to find, but did come across these,

There is a companion wiki article on the UK 2014 Budget.

A loan involves a bank giving someone a wedge of cash in exchange for an agreed periodic payment.

An annuity involves a bank giving someone an agreed periodic payment in exchange for a wedge of cash.

They are the same thing! So we should be able to price them the same way.