Sigmoid Hall age 40 years old was lying on his living room suite, wondering how he was going to save given the recent increase in his rent, when the telephone rang. It was his landlord at the other end of the line with more bad news; not only had the rent increased but the house which Sigmoid occupied was now up for sale. The landlord offered him the first right of refusal in purchasing the property. Sigmoid had mixed feelings as he had always dreamt of owning a similar house but knew that he could only come up with the required deposit of $50,000.00; He wondered how he would fund the full purchase price of $350,000.00. A short call to his local building society presented him with the following mortgage choices: 25 years at an interest rate of 5.5% or 30 years at an interest rate 5.75%; each with monthly compounding. As he sat thinking of how he could meet the minimum mortgage payment he was mindful that his employment contract stipulated a required retirement age of 60 years old with a provision for an extension of no more than an additional 5 years, that is, to 65 years old. As Sigmoid wondered aloud whether or not he would still be paying mortgage when he retired, his wife reminded him about the bond that his aunt had willed to him. A quick reading showed that the bond was a zero coupon instrument with the following provisions: Encashment in 20 years (when Sigmoid would be 60 years old) for a value $99,000.00 or encashment at maturity in 25 years (when Sigmoid is 65 years old) with the full face value of $130,000.00. You are a Mortgage Broker and Sigmoid has now asked you to advise him which bond encashment date will allow him to make the minimum feasible payment while allowing him to buy a car for $10,000.00 and repay his mortgage on retirement. (a) Use amortisation tables to show his balance at the end of three months under each mortgage option. b) Which mortgage option and bond encashment date should he choose bearing in mind the criteria that he has laid out? Will he need to apply to retire at age 65? Show all workings to support your answer. c) How much interest will he pay with his chosen option?