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. [2 marks] Calculate the total amount Sophie would pay, using option 1. [2 marks] Calculate the number of months it will take to repay the mortgage using [3 marks] ption 2 Il

The monthly repayment using option 1 would be $1326.65, the total amount Sophie would pay using option 1 would be $318,395.72, and she will never be able to repay the mortgage using option 2.

Mortgages

Given that Sophie is planning to buy a house, and she needs to take out a mortgage for 120,000, and 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.

To A) calculate the monthly repayment using option 1, B) calculate the total amount Sophie would pay, using option 1, and C) calculate the number of months it will take to repay the mortgage using option 2, the following calculations must be performed :

A and B)

120000 x 1.05^20 = X
318,395.72 = X
318,395.72 / (20 x 12) = X
1326.65 = X

C)

120000 x 1.06^20 = 384,856.25
20 x 12 x 1000 = 240,000
120000 x 1.06^30 = 689,218.94
30 x 12 x 1000 = 360,000
120000 x 1.06^10 = 214,901.72
10 x 12 x 1000 = 120,000
Therefore, she will never be able to cover the amount of the loan by paying $1000 per month.

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