Question 1 (20%- Please use 6 decimals)

Helen is a business woman and goes to the local bank for a 4-year loan for her new business. The loan repayment will be quarterly (4 times a year, every 3 months) with 0.09 yearly interest bot with monthly frequency of compounding. The loan amount given to her is exactly 1.000.000 Euros, the first 4 payments equal zero (so repayment during the first year will help the new business that will have too little cash in the beginning). So she will make 12 payments to the bank, the first 11 payments will be equal to each other and exactly 70000 Euros each. What is the exact amount of the last payment to be paid at the end of the loan repayment period? What is the interest payment and what is the principal repayment in the first payment that she will actually make to the bank ?

Annuity: