help with following question:

1. Consider the following zero-coupon yield curve for U.S. Treasury: Maturity (years) 2 3 4 5 Zero-Coupon YTM 3.25% 3.50% 3.90% 4.25% 4.40% a. What is the price of a five-year default-free security with a face value of $1000 and an annual coupon rate of 5%? b. What is the YTM of the bond? 2. You are planning to buy a house worth $500,000 today. You have $100,000 savings for the down payment. A 30-year fixed-rate mortgage is 6.00% APR. a. Suppose if you take the 30-year loan, how much is your monthly payment? b. Show the payment for interest and principal separately for the first three months. c. Ten years later, the 30-year fixed-rate mortgage rate reduces to 3% APR. So you decide to refinance the debt with a new 30-year fixed-rate loan. How much is the new monthly payment