I need the formula and explanations for the attached questions real estate finance and investments

Formula and explanations CHAPTER 6 Mortgages: Additional Concepts, Analysis, and Applications MULTIPLE CHOICE 1. A house is for sale for $250,000. You have a choice of two 20-year mortgage loans with monthly payments: (1) if you make a down payment of $25,000, you can obtain a loan with a 6% rate of interest or (2) if you make a down payment of $50,000, you can obtain a loan with a 5% rate of interest. What is the effective annual rate of interest on the additional $25,000 borrowed on the first loan? (C) (A) 1.00% (B) 6.00% (C) 12.95% (D) 18.67% (E) 20.10% 2. A borrower has secured a 30 year, $150,000 loan at 7% with monthly payments. Fifteen years later, the borrower has the opportunity to refinance with a fifteen year mortgage at 6%. However, the up front fees, which will be paid in cash, are $2,500. What is the return on investment if the borrower expects to remain in the home for the next fifteen years? (E) (A) 6.00% (B) 7.00% (C) 13.00% (D) 22.62% (E) 28.89% 3. A borrower has secured a 30 year, $150,000 loan at 7% with monthly payments. Fifteen years later, an investor wants to purchase the loan from the lender. If market interest rates are 5%, what would the investor be willing to pay for the loan? (C) (A) $75,000 (B) $111,028 (C) $118,478 (D) $168,646 4. A borrower is purchasing a property for $180,000 and can choose between two possible loan alternatives. The first is a 90% loan for 25 years at 9% interest and 1 point and the second is a 95% loan for 25 years at 9.25% interest and 1 point. Assuming the loan will be held to maturity, what is the incremental cost of borrowing the extra money? (A) (A) 13.66% (B) 13.50% (C) 14.34% (D) 12.01% -1