Present Value. Use a calculator for each of these problems.

(a) You are moving to Bozeman and you are going to stay here forever. You would like to find an apartment. You can either buy it or rent it. The monthly rent is $500 and the monthly interest rate is 0.1%. Alternatively, you can purchase the apartment, paying $600,000. How are you going to finance your new accommodation? Argue using the PV formula.

(b) You take a loan to buy a car that costs $4000. What is your monthly payment if you want to pay back the loan after 3 years (36 payments) and the monthly interest rate is 0.5%. (Hint: think annuity)

(c) You are hired by Merrill Lynch to help assess the value of a T-bond (a bond issued by the Treasury Department) with the face value F=$1000, coupon c = $100 (paid anually until T 1 and face value F paid at time T) and time to maturity equal to T = 10 years. The interest rate is equal to r = 10%. Find the PV of such a bond. Is it a good or bad deal to buy such a bond for $900? Explain.

(d) You want to receive $40,000 per year when retired (you will be retired from 61-80). How much do you have to save between 21-60 years if the interest rate is 5%?

(e) You save $20,000 per year when working and plan to work from 21-60. How much will you consume per year when you retire? Assume you will be retired from 61-80. The interest rate is 5%.