8a. [2 marks]
Sophie is planning to buy a house. She needs to take out a mortgage for $120000. She is considering two possible options.
Option 1: Repay the mortgage over 20 years, at an annual interest rate of 5%, compounded annually.
Option 2: Pay $1000 every month, at an annual interest rate of 6%, compounded annually, until the loan is fully repaid.
Calculate the monthly repayment using option 1.
8b. [2 marks]
Calculate the total amount Sophie would pay, using option 1.
8c. [3 marks]
Calculate the number of months it will take to repay the mortgage using option 2.
8d. [2 marks]
Calculate the total amount Sophie would pay, using option 2.
8e. [1 mark]
Give a reason why Sophie might choose
option 1.
8f. [1 mark]
option 2.
8g. [2 marks]
Sophie decides to choose option 1. At the end of 10 years, the interest rate is changed to 7%, compounded annually.
Use your answer to part (a)(i) to calculate the amount remaining on her mortgage after the first 10 years.
8h. [2 marks]
Hence calculate her monthly repayment for the final 10 years.
