Tamara has a mortgage for $526,158.00. The term of the mortgage is 5 years, and the amortization period is 15 years. Tamara will make monthly payments and the mortgage rate is r⁽¹⁾ = 9.250%. After 3 years, the interest rate drops to 7.750% compounded annually, and she decides to refinance her loan. In order to refinance, she has to pay a penalty of 3 months' interest (based on the original interest rate), which is added to the outstanding balance on the new mortgage.

a) What is the outstanding balance at the time Tamara decides to refinance (not including the penalty)?

b) What is the amount of the penalty?

c) The new mortgage has exactly the same terms (term, amortization period, etc.) as the original mortgage except for the amount and the interest rate. What are the new monthly payments?