Assume that Juul has decided to repay a bank loan with a amortization schedule. The loan is for the amount of 225,000 at the present day. Payments are made by the end of each month. The first payment is 2000 with each sequence payment 5 less than the previous one, except the last one being the remaining debt. The nominal interest to be paid on the remainder is 3% per year. (a.) How long will it take Juul to repay the loan completely? How much is the last payment? Attach a table containing the remainders, interet paid and redemption on this loan for each month in the appendix. (5 pts) (b.) After 10 years, Juul decides to improve her finance by repay this loan within the next year. Under the updated agreement, she has to pay 5,439.20 at the end of next 12 months. Determine the effective annual interest rate of this scheme. [Hint: use the rootSolve package in R.] (5 pts)