Suppose you agreed to purchase a house for $100,000. In your loan application, you requested a loan-to-value ratio of 90%. The mortgage contract calls for an interest rate of 6%, a 20-year term, and an amortization period of 30 years. In addition, the lender charges 5 points, which is deducted upfront. You also spend $500 renovating the house.

Calculate the (1) face value of the loan, (2) the actual loan amount advanced by (lender, and (3) total amount of equity you need to invest in the house

Calculate the monthly payment and mortgage balance at end of the 5th-year mortgage

Assume you prepay the loan at end of the 5th year, calculate the annual percentage rate (APR), effective interest rate (EIR), effective Annualized Yield (EAY), and the bond equivalent yield (BEY). In the case of BEY assume bonds in the capital markets pay coupon quarterly rather than semiannually

Assume you are at the end of year 5 and the market interest rate for mortgage of similar risk is 4%. First, calculate the market value of the loan, and then capital gain or loss incurred by the lender. 6 points)