Lucy currently purchased a home with a 30-year fixed rate mortgage with the loan amount of $930,000 at an annual rate of 5.25% in early May 2023. The refinance cost is $5,000 and she is watching the interest rates in order to refinance when the rate is lower.

Required

a. What is the highest annual rate that can start her to refinance after one year if she needs her future monthly payment be at least 400 lower than before? 

b. What is the highest annual that can start her to refinance after one year if she needs an annual effective cost of at most 5% on the refinancing? Lucy plans to hold the property till the end of September 2029. Hint: this rate is higher than part a. 

c. If after one year, Lucy finds that the interest rate is not going to drop, Lucy prepays on her loan with $100,000 at the end of year 1. What is the return (IRR) on this $100, 000 investment if Lucy holds the property for just another year (at the end of year 2)? Assume that we have no other costs except mortgage payments. After prepayment, the interest can be approximately calculated by annual for approximation.