Optimal Consumption, Taxes, and Fixed Rate Mortgage

Optimal consumption and taxes

Question 1: Optimal consumption and taxes (7 marks)You just turned 27 (January 1st) and have $15,000 in savings. Your current is salary $65,000 whichyou expect to grow at a real rate of 1.75% per year until you retire. You are paid on an annualbasis with wages being received at the end of each year. Assume that you will retire when you turn67 and that you will die on your 95th birthday. Your current level of subsistence consumption is$20,000 per year. You are prudent and want to your total standard of living to increase by 1.25%per year in real terms until you retire. After you retire you want your total standard of living todecline by 1% per year (real rate). Assume that the real valuation rate is 4% per year and that youpay taxes according to the following (hypothetical) tax system:Taxable Income Levels Average Tax Rate$0 to $20,0000%$20,000.01 to $70,00015%$70,000.01 to $100,00025%>$100,00035%Part A:Please compute your current optimal consumption, assuming that all cash flows take placeat the end of the year.You should also assume that: i) you are not taxed on investment income, i.e., you only need toaccount for taxes on wage income and ii) this tax system offers no tax credits or deductions andhas no surtax.1

Question 2: Fixed Rate Mortgage (8 marks)Hazel has $100,000 in savings that she plans to use as a down payment on a house that costs$650,000. She selects an closed, fixed rate mortgage with a 3-year term, a 20 year amortizationperiod and an interest rate of 4.5% (APR). In addition, she will make monthly payments.Part A:Please compute her monthly payments.Part B:How much principal is left after her term expires (i.e., after 3 years)?Part C:Assume that, after one year of payments, interest rates drop to 3.0% APR. Should she breakthe mortgage and refinance at the new rate? Please show all relevant calculations and explain anyfactors that might influence the decision. Do not forget to state any assumptions