Suppose that you would like to buy a small apartment 3 years from today. The price of the apartment in 3 years will be $200,000. You talked to a bank, and this is what the bank has offered you: If you make a down payment of 10% of the purchase price, you will be able to borrow the rest from the bank at an APR of 10% compounded monthly (the down payment has to be exactly 10% of the purchase price). However, if you make a down payment of 15% of the purchase price, you can take the loan at an APR of 9% compounded monthly (the down payment has to be exactly 15% of the purchase price). The payments will be semi-annual, and the first payment will take place 6 months after you take out the loan. The loan needs to be paid back in 5 years (i.e., you will make 10 equal mortgage payments). Ideally, you would like to pay the lowest interest. You deposit $20,000 in an account today. The account has an APR of 8% compounded quarterly. The amount you will have in three years will be used towards the down payment of the house. Three years have passed. You make the down payment, and take the loan. How much do you need to pay for each mortgage payment? You have to show your work to get credit