Question 1. You are a loan manager at MAT133 Bank. Your client, Jordan, is setting up a new small business and takes out a loan from your bank for $100,000 on October 1, 2023. You offer Jordan the following repayment scheme: Payments are to be made at the beginning of each month, starting October 1, 2024. The loan accrues interest at a reduced APR of 7%, compounding at the end of each month in the first year. The loan then accrues interest at an APR of 10%, compounding at the end of each month starting in the second year (October 2024) and onward.

(a) Jordan wants his last payment to be on September 1, 2039. Calculate Jordans monthly payment. (Round your answer to the nearest cent.)

(b) After five years, Jordans business is very successful, and he can afford to pay more each month. Suppose he doubles his monthly payments starting October 1, 2029. When would Jordans last payment be?

Question 2. 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 do 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.