Your mother retired today and has the option of purchasing an annuity. If she exchanges $$23,000$ of her savings today for a $6\mathrm{.}50$ percent, $11-$year annulty, what will her annual cash flow be$?($Unless stated otherwise, always assume the first payment is received at the end of the period, not the start$).$

NOTE: You are exchanging cash today for a series of cash flows. This is an annuity problem $($chapter $6),$ where we the value of the annuity is defined at the START of all the cash flows, so use the present value of an annulty equation $P{V}_A=C\frac{1-(1+r{)}^{-N}}{r}.$ You already know what the annuity is worth today $(($:$P{V}_A\},$ the number of payments $($t$),$ as well as the discount rate $(r).$ You only need to calculate $C,$ the size of the cash flow.

Multiple Choice

$$2,090\mathrm{.}91$

$$5,136\mathrm{.}62$

$$2,842\mathrm{.}13$

$$2,991\mathrm{.}27$