It is January 1st, 2021, and you are setting up a perpetuity that will allow you to withdraw R dollars at the end of April and October every year, forever. Suppose that the stated APR of the perpetuity is r > 0.

Question 1 Determine the present value of the perpetuity if interest is compounded monthly. Leave your answer in terms of R and r.

Question 2 Determine the present value of the perpetuity if interest is compounded continuously instead. Leave your answer in terms of R and r.

Question 3 Which of your answers (between Question 1 and Question 2) do you expect to be larger? This question will be hard to answer mathematically, but you should be able to argue it using financial reasoning. In 5 sentences or less, justify your answer.