Work through the mortgage scenario for four parts:

1. Borrower has a 30 year mortgage at 6% based on $800,000. What is the monthly principal and interest payment of this mortgage?
2. After 8 years what is the remaining balance?
3. At the end of the eight year (based on remaining balance found in Number 2 above), the borrower has the ability to refinance that remaining balance with a 20 year mortgage with an interest rate of 4%. If the balance in Number 2 above is refinanced with a 20 year mortgage with an interest rate of 4% what would the new monthly principal and interest payment be for this new loan?
4. Assuming that there is a prepayment penalty of $12000 to pay off the original mortgage used in Number 1 (based on 30 years, 6%, $800000) and $10000 in costs to obtain the new loan, how many months would you need to hold the property with the new mortgage as described in Number 3 to offset the costs of the refinance.

Please provide me answers to all the four questions.

Thanks