Today is January 1, 2021. Benny borrows from Jessica $239,037 and agrees repay her by monthly installments. Payments will increase at a rate of 0.5% per month. The first payment of $1,000 is to be made exactly one month from today. However, after Jessica has worked out the time it will take for the entire loan to be repaid, she thinks it is too long. She proposes cutting the repayment time in half. Also, instead of growing payments, Jessica prefers a constant amount paid at the end of each quarter. The effective annual interest rate is 10%.

a) Determine how much time it takes Benny to repay the loan under his proposal. Round your answer to the nearest number of months. (Hint: ln xy = y ln x) (4 marks)

b) Find the amount Jessica prefers to receive at the end of each quarter under her new proposal. Ignore your answer in part a) and assume it to be 420 months. (4 marks)

c) Calculate the amount of interest Benny will have paid over the life of the loan. (2 marks)