How to derive the present value formula for annuity and perpetuity

The video discusses annuities and perpetuities. It explains that an annuity consists of equal payments made at regular intervals, differentiating between ordinary annuities (payments at the end of a period) and annuities due (payments at the beginning). The example given involves receiving $100 for seven years, and the video walks through the calculation of the present value of this ordinary annuity using discounting factors. It illustrates how to derive the equation for the sum of the annuity payments, taking into account the number of years (N) and the discount rate (r). Finally, it touches on perpetuities, where the payment series extends to infinity, leading to the conclusion of how to find the present value in such cases. Overall, the video aims to provide a clear understanding of these financial concepts and their mathematical derivations.