On January 1, 2024, you are setting up a perpetuity where you can withdraw $20000 at the end of every quarter where the first withdrawal occurs on March 31, 2024. To achieve this, you make an initial deposit of A into an account where interest is compounded at the end of each month at an APR of r.

(a) Determine A in terms of r.

(b) The terms of the perpetuity change after 10 years, so that interest is to be compounded continuously at an APR of r instead.

Determine which of the two following statements is true, and justify your answer.

Statement A: You need to deposit a lump sum into the account at the 10-year mark so that you can still receive the quarterly payments of $20000. Statement B: The revised terms of the perpetuity allow you to withdraw more money every quarter without adding any more money into the account.