- The Royal Bank of Poundland offers mortgages at a basic rate of 6% interest, charged monthly As a special offer, it offers new customers two-part mortgages, where the first 15,000 of the loan are charged at 3% interest and the rest is charged at the basic rate. As part of the deal, customers must make monthly payments, and two thirds of their monthly payment must go toward the first part of the loan. First-time buyer A wishes to borrow 60,000 to buy a house using the special offer. a. What will be the initial balance of the two parts of the loan when it is first taken out? [2 marks] b. Buyer A is able to make fixed monthly repayments of 600 per month. Write a linear difference equation describing how the balance of the two parts of the loan change over time. [5 marks] c. What will be the total balance of the mortgage after six months? [6 marks] d. Explain what is meant by the controllability of a dynamic system. [4 marks] e. Using your linear difference equation from Question 6.b, check the con- trollability of this system. Comment on the affordability of the loan scheme for buyer A. - The Royal Bank of Poundland offers mortgages at a basic rate of 6% interest, charged monthly As a special offer, it offers new customers two-part mortgages, where the first 15,000 of the loan are charged at 3% interest and the rest is charged at the basic rate. As part of the deal, customers must make monthly payments, and two thirds of their monthly payment must go toward the first part of the loan. First-time buyer A wishes to borrow 60,000 to buy a house using the special offer. a. What will be the initial balance of the two parts of the loan when it is first taken out? [2 marks] b. Buyer A is able to make fixed monthly repayments of 600 per month. Write a linear difference equation describing how the balance of the two parts of the loan change over time. [5 marks] c. What will be the total balance of the mortgage after six months? [6 marks] d. Explain what is meant by the controllability of a dynamic system. [4 marks] e. Using your linear difference equation from Question 6.b, check the con- trollability of this system. Comment on the affordability of the loan scheme for buyer A