Problem 1. You decide to open a money market account to save for a down payment on a new home (typically 20% of the price of the home). You make an initial deposit of $2500 to open the account and promptly forget about the account, never making another deposit.
(a) If the money grows at a nominal annual interest rate of 3% compounded monthly, how much money is in the account at the end of 5 years?
(b) Calculate the APY on the money market account assuming an APR of 12%.
(c) Briefly explain why the bank may prefer to advertise the APY on a savings account or money market account but advertise the APR on a mortgage.
Problem 2. Reconsider Problem 1. What is the value of the money market account after 5 years if you make an initial deposit of $100 to open the account and monthly deposits of $100? Assume the nominal annual interest rate is 3% compounded monthly.
Problem 3. Calculate the monthly payment (i.e., principal and interest only) on a $250,000, 30-year mortgage if the APR is (a) 4%, (b) 8%, and (c) 14%. Comment on how you think changes in the 30-year mortgage APR between 1980 (APR ≈ 14%) and 2017 (APR ≈ 4%) affected the housing market.