please give full explanantion

a) You are 35 years old today and are considering your retirement needs. You expect to retire at age 65 (in 30 years) and you plan to live to age 99. You want to buy a house costing $300,000 on your 65 th birthday and your living expenses will be $30,000 a year after that (starting at the end of year 65 and continuing through the end of year 99, i.e. for 35 years). Assume an annual interest rate of 8%, annual compounding: i) How much will you need to have saved by your retirement date to be able to afford this course of action? ii) Suppose you already have $50,000 in savings today. If you can invest money at 8% a year, how much would you need to save at the end of each year for the next 30 years to be able to afford this retirement plan? (5+10=15 marks) b) You bought a house a year ago for $250,000, borrowing $200,000 at quoted rate of 12% annual from TD bank, with semi-annual compounding, on a 25 -year loan. Interest rates have since come down to 9%. You can refinance your mortgage at this new rate. i) How much are your monthly payments on your current loan (at 12%) ? (5 marks) ii) How would your monthly payments change if you could refinance your mortgage at 9% (with a 24-year term loan)? (5 marks) iii) Suppose you kept your monthly payments at the original amount found above at 12%, but refinanced at 9%, how long would it take you to pay off your mortgage? (5 marks) (15+15=30 marks )