Sofia just found her dream home after finishing her business degree. The house costs $500,000. She is still in debt from college and has no savings. Because of her excellent credit, the bank requires her to put down only 5% of the cost of the house. She currently makes $10,000 a month. Assume no taxes, fees, etc.

a) If Sofia can put 20% of her salary each month in an account earning 1.2% APR (monthly compounding), approximately how many months will it take to accumulate the amount needed for the down payment.

b) Assume that by the time she has all the money needed for down payment for the house (or a comparable one) is still available, and costs the same.

- If the bank charges her a 4.8% APR (monthly compounding) on a 30-year fixed interest loan, to be repaid in equal monthly payments, how much is Sofia's monthly payment?