You have decided to invest in the Santa Clara housing market and buy a small house. Your new small home on California Avenue costs $2,000,000. You get a mortgage loan from your bank. Assume that interests are compounded monthly and the current annual interest rate is 4.8%. The term of your mortgage is 30 years. For full credit you should show both the analytical and numerical form of the solutions. 1. What is the monthly mortgage payment such that you can pay off the loan in 30 years. (Your first payment is made at the end of the first month. Assume interest rates are constant for the whole time horizon.) If you cannot find a solution to this problem, use the number $10,000 for the monthly payments for the other questions. Note, that this number is not identical to the solution of this question. 2. What will be the mortgage balance after 10 years? 3. Consider an alternative scenario. At time t=0 you are worried about the high monthly payments for your mortgage. Therefore you ask your bank for a balloon mortgage instead of the conventional mortgage. In a balloon mortgage a large portion of the borrowed principal is repaid in a single payment at the end of the loan period. What is the amount of money that you need to repay at the end of your mortgage (30 years), if you want to make only half the monthly payments of the conventional mortgage (in part 1.) for the other months. Assume that the interest rate stays constant at 4.8% for the whole time period. Hint: You can use the formula for the geometric sum. For R=1 it holds that Sn(R)=i=0n1Ri=1R1Rn