William would like to purchase a house worth $350,000. He can afford to make a down payment of $50,000 and needs to take out a mortgage. The bank offers him a 35-year mortgage with monthly payments. The interest rate is 7% APR with semi-annual compounding. a) What will be his monthly payments? b) He can only afford to make payments of $ 1500 per month. The bank agrees to this provided he pays the remaining amount in a lump sum fashion at the end of 35 years. How much will he have to pay lump sum at the end of 35 years?