"short cut" formula for present value of an annuity

CFA text volume 5, reading 70 (p 533) references a “short cut formula” that can be used to compute the value of a bond when using a single disconunt rate: “Compute the present value of the annuity and then add the present value of the maturity value.” It then proceeds to give a formula for the present value of an annuity: annuity payment x (1-(1/(1+i)^no. of periods)/i) I am trying without success to tie this formula back to the formula I know for the present value of an annuity, which is simply the sum of each payment divided by (1+i)n for whatever number n represents in the case of that payment. Anyone know how the formula above is derived? And do we need to know this formula (I didn’t see it in Schweser)?

This formula was introduced in volume 1 under quants (time value of money reading I think, or the next one) you can google for the derivation, I think wiki has a pretty good piece on it too