1.1 We are currently at year 0. Consider a perpetuity that pays $100 at the end of year 6 and thereafter every 5 years (i.e. at end of year 11, year 16, year 21 and etc) with cash flows growing at an annual compounded constant growth rate of 2% per year from end of year 6 onward. The term structure is flat at 10% per year. Determine the present value of the perpetuity.

1.2 You have just purchased a house in Singapore for $1 million, using your own savings to make a down payment equal to 20% of the houses value, with the remainder financed via a 25-year mortgage. The mortgage has fixed monthly payments, with the first payment due in exactly one month. The stated annual interest rate on the loan is 4% with monthly compounding. What is the total interest paid by you at the end of year 5 immediately after the 60^th monthly mortgage payment? If you repay $100,000 of your loan at this point (i.e. immediately after the 60^th monthly mortgage payment), what will be the revised monthly mortgage assuming the interest rate remain the same