1. You want to buy a house and take out a mortgage for $250,000. The only mortgage that you can afford is a 30 year ARM that has a fixed rate of 3% annual compounded monthly for the first 3 years and then can adjust every year after that. Against the advice of a wise EMIS professor that you once had, you decided to take the mortgage.
a) What is the monthly payment for his home mortgage for the first 3 years?
After you make the 36th payment, the interest rate adjusts to 5% annual compounded monthly.
b) What is the new monthly payment?
After you make the next 12 payments, the interest rate increases to 7% annual compounded monthly.
c) What is the new monthly payment?
You make the next 12 payments and the interest rate is about to adjust again. You decide that your old EMIS professor was right all along and you take out a new loan with a fixed interest rate of 4.5% annual compounded monthly for a term of 20 years.
d) What is the total amount of interest that you will pay for all of the mortgages (ARM plus fixed rate loans)?
2. You are looking to purchase a new vehicle for $24,500. This vehicle gets 21 mpg and you average driving 15,000 miles per year. You expect that gasoline will average $2.40 per gallon for the first year and will increase 15% per year but it will never get above $5 per gallon because of government controls. Maintenance is included for the first two years but after that you think that maintenance will cost $1,000 and increase by 10% per year after that. The vehicle will lose 30% of its value the first year but the salvage value will only decrease by 10% per year after that. For an interest rate of 6%, what is the economic life of the vehicle?