You are planning to buy a house worth $500,000 today. You plan to live there for 15 years and then sell it. Suppose you have $100,000 savings for the down payment. There are two financing options: a 15-year fixed-rate mortgage (4.00% APR) and a 30-year fixed-rate mortgage (5.00% APR). The benefit of borrowing a 30-year loan is that the monthly payment is lower. But since you only plan to hold the house for 15 years, when you sell the house you still owe the bank and you have to use part of the proceeds to repay the loan. Suppose if you take the 30-year loan, you can use the money saved from the lower monthly payment to invest in a stock portfolio that generates 10% annual return (APR). Which loan should you take? With proper formulas

a. What is the monthly payment if you take the 15-year loan?

b. What is the monthly payment if you take the 30-year loan?

c. What is the remaining balance of the 30-year loan at the end of 15 years ?

d. If you take the 30-year loan and use the money saved from the lower monthly payment (compared with that of a 15-year loan) to invest in the stock market and earn 10% annual return (APR), how much do you expect to have in your investment account at the end of 15 years?

e. Suppose you take the 30-year loan, use the money saved from the lower monthly payment to invest in the stock market as in (d), and sell the house for $700,000 in 15 years, how much money do you have after repaying the remaining loan amount?

f. Compared with the other option, where you take the 15-year loan and sell the house at the end of 15 years for $700,000, which option is better?