Present Value of Annuities and Perpetuities

Jessica is considering two different investment options that involve receiving cash flows over time. The first option is a five-year annuity that pays $5,000 at the end of each year. The second option is a perpetuity that pays $2,000 annually, beginning in year six. If Jessica plans to evaluate these options at a discount rate of 6%, how should she determine the present value of each option in order to make an informed investment decision?

To calculate the present value (PV) of the annuity and the perpetuity, she will use the formulas: for the annuity, $$PV = P imes\frac{1 - (1 + r)^{-n}}{r}$$; and for the perpetuity, $$PV =\frac{P}{r}$$. Here, $P$ is the payment, $r$ is the discount rate, and $n$ is the number of years.