You have been offered the opportunity to buy an investment that pays guaranteed cash flows every year for a fixed period of time $($ie$,$ an annuity$).$ There are two products available to you:

Option A: pays guaranteed cash flows of $$710$ per year for the next $15$ years.

Option B: pays guaranteed cash flows of $$710$ per year forever!

What is the most that you should you be willing to pay for these investments today if you need to earn a rate of return of $6\mathrm{.}0\%?$

a$)$ The most you should be willing to pay for Option A should be:$($Round to two decimal places.$)$

b$)$ The most you should be willing to pay for Option B should be:$($Round to two decimal places.$)$

d$)$ Draw a conclusion based on your analysis here: how does the length of time that we expect to receive cash flows affect our estimate of their value? $($Choose the best answer from the list below$)$

$1.$ Cash flows that last for a LONGER period of time appear to have LESS value, all else held equal

$2.$ No opinion $/$ not sure how to think about this

$3.$ Cash flows that last for a LONGER period of time appear to have MORE value, all else held equal

$4.$ The value of these cash flows does NOT appear to change as the time period increases, it may not matter