please help me answer questions A,B,C,D, and E

also could you please show all your work, thank you!

Suppose that five years ago you took a mortgage loan for $160,000 at 7.750% for 30 years, monthly payments. This loan has a prepayment penalty of 5% of the outstanding balance for the first six years of life. The market rate on new mortgages now is 6.00%. Lenders are charging 6% financing costs on new loans. Your opportunity cost is 6.00%. A. If you plan to hold the loan to maturity (whether refinancing takes place or not), should you refinance if you want to refinance the payoff of the existing loan for the remaining term of the existing loan? B. Should you refinance if you wish to refinance the payoff of the existing loan for 15 years? Assume that the contract rate on the new loan remains at 6.00% and the loan is held to maturity. C. Suppose you want to have no out-of-pocket expenses and you want to extend the term on the new loan to 30 years. Should you refinance? Assume the contract rate on the new loan remains at 6.00% and the loan is held to maturity. D. Assume the conditions in part A except that you know that the holding period of the loan will only be six years. Should you refinance? Assume the contract rate on the new loan remains at 6.00% E. Suppose you want to take $30,000 of equity out of the house and you want no out-of-pocket expenses. Should you refinance for a 20-year term? Assume that the contract rate on the new loan remains at 6.00% and the loan is held to maturity. Suppose that five years ago you took a mortgage loan for $160,000 at 7.750% for 30 years, monthly payments. This loan has a prepayment penalty of 5% of the outstanding balance for the first six years of life. The market rate on new mortgages now is 6.00%. Lenders are charging 6% financing costs on new loans. Your opportunity cost is 6.00%. A. If you plan to hold the loan to maturity (whether refinancing takes place or not), should you refinance if you want to refinance the payoff of the existing loan for the remaining term of the existing loan? B. Should you refinance if you wish to refinance the payoff of the existing loan for 15 years? Assume that the contract rate on the new loan remains at 6.00% and the loan is held to maturity. C. Suppose you want to have no out-of-pocket expenses and you want to extend the term on the new loan to 30 years. Should you refinance? Assume the contract rate on the new loan remains at 6.00% and the loan is held to maturity. D. Assume the conditions in part A except that you know that the holding period of the loan will only be six years. Should you refinance? Assume the contract rate on the new loan remains at 6.00% E. Suppose you want to take $30,000 of equity out of the house and you want no out-of-pocket expenses. Should you refinance for a 20-year term? Assume that the contract rate on the new loan remains at 6.00% and the loan is held to maturity