You have two goals for which you want to save - both relating to a home purchase. Realizing the ambitiousness of your goals you have decided to start a savings plan. First, you want to purchase your new $500,000 home in eight years. Your first goal is to have $100,000 saved for a down payment and you will finance the rest with a 30- year, 6% (APR) conventional (simple amortized) mortgage. Second, you also want to pay off the home 15 years after purchase, but you do not want to be committed to a higher 15-year mortgage payment. So, separate from making your monthly payment, your second goal is you want to save enough money to make a final, lump-sum payment, sent as payment #181, to pay off the balance remaining at that time. You want to invest on a monthly basis beginning one month from now and ending when you pay off the mortgage, as one continuous annuity. Assume you can earn 8% (EAR) on your investment. Calculate the monthly savings contribution required to meet your two goals. (18 points.)