Isabelle takes out a loan of $250,000 to buy an apartment. The loan is for 20 years and the nominal annual interest rate is 3.8%, compounded monthly. Isabelle makes fixed monthly payments at the end of each month.

(a) (i) Calculate the fixed monthly payment Isabelle needs to make.
(ii) Calculate the total amount Isabelle will pay back over the 20 years. [5 marks]

After 5 years, Isabelle decides to refinance the loan. The remaining balance will be paid off over a new period of 10 years with a new nominal annual interest rate of 3.5%, compounded monthly. She will continue to make fixed monthly payments.

(b) Calculate the remaining balance on the original loan after 5 years (60 payments). [3 marks]
(c) Calculate the new fixed monthly payment for the refinanced loan. [3 marks]
(d) Calculate the total amount Isabelle will save by refinancing the loan compared to staying with the original loan terms. Give your answer to the nearest dollar. [5 marks]