QUESTION 1 (28 marks for STAT2032, 34 marks for STAT6046) Three years ago, Thena bought an apartment with a $300,000 mortgage from Eternal Bank. She needs to pay off in equal monthly instalments over 30 years. At that time, the interest rate was fixed at 7.00% effective p.a. for the next 3 years. Now three years have passed, and the remaining 27 years of the loan have come up for renewal at an updated interest rate. Unfortunately, Eternal Bank increases Thena's mortgage interest rate to 8.75% effective p.a. (fixed for the remainder of the loan). a) i. Calculate the resulting increase in Thena's monthly payments. Show all your workings. ii. Calculate the additional interest that Thena needs to pay due to this increase in interest rate, for the remaining term of the loan. Show all your workings. (Hint: express the answer in nominal dollars paid, rather than in present or accumulated value.) iii. Insert one Excel scatter plot. This plot needs to contain the amount of the monthly payment, monthly interest, and monthly principal repaid for the remaining term of the loan, based on the updated interest rate. Clearly label all the axes and lines. QUESTION 1 (28 marks for STAT2032, 34 marks for STAT6046) Three years ago, Thena bought an apartment with a $300,000 mortgage from Eternal Bank. She needs to pay off in equal monthly instalments over 30 years. At that time, the interest rate was fixed at 7.00% effective p.a. for the next 3 years. Now three years have passed, and the remaining 27 years of the loan have come up for renewal at an updated interest rate. Unfortunately, Eternal Bank increases Thena's mortgage interest rate to 8.75% effective p.a. (fixed for the remainder of the loan). a) i. Calculate the resulting increase in Thena's monthly payments. Show all your workings. ii. Calculate the additional interest that Thena needs to pay due to this increase in interest rate, for the remaining term of the loan. Show all your workings. (Hint: express the answer in nominal dollars paid, rather than in present or accumulated value.) iii. Insert one Excel scatter plot. This plot needs to contain the amount of the monthly payment, monthly interest, and monthly principal repaid for the remaining term of the loan, based on the updated interest rate. Clearly label all the axes and lines