Reference no: EM133006266

Question - Today is 1 January 2021. Jane is 20 years old today and she is planning to purchase real estate with the price of $800,000 on 1 January 2028. Jane believes that, at the time of purchasing the house, she should have savings to cover 20% of the house price (i.e., $160,000). She can then borrow the remaining 80% of the house price (i.e., $640,000) through a 10-year mortgage (which starts on 1 January 2028) from MQU Bank at an interest rate of 6% p.a. convertible monthly. The loan is taken out on 1 January 2028. Jane has two repayment options. 1. Repay the loan with level repayments by the end of each month. The loan will be fully repaid after 10 years. 2. Repay the loan with a series of increasing repayments made by the end of each month. After the repayments in first year, the following repayments will increase by 5% at the end of every 12 months. For example, if the monthly repayment in the first year is $3,000 per month, then the monthly repayment will be $3,000×1.05 in year 2, $3,000×1.05×1.05 in year 3 and etc. The loan will be fully repaid after 10 years.

a) For the above two repayment options, calculate the first repayment amount.

b) For the above two repayment options, calculate the loan outstanding amount after 1 year from 1 January 2029.