At the end of 2014, after 5 years of hard working, John was able to purchase his first home with a deposit of $150,000. The bank agreed to lend him 80% of the value of his home for 25 years at an interest rate of 4% per annum, fixed for the first five years. After a long search, John was able to secure a two-bedroom apartment in one of the suburbs close to his work.

a) What is the price of his two-bedroom apartment assuming that he can only pay for the apartment using his own money and what the bank is willing to lend? How much does he borrow? (2 marks)

b) What is his monthly repayment assuming that John wants to pay principal and interest, the first repayment happens at the end of the month and he takes out the loan on 1st January 2015? (3 marks)

c) 5 years later, on the 1st January 2020, his fixed rate expires and the variable interest rate is now 10% per annum, while the fixed rate for 5 years is 13%. John decides to go with the variable rate option as the fixed rate is too high. What is his new repayment? (5 marks)

d) John realises that he cannot afford the new monthly repayment, so he goes to the bank and negotiates. The bank agrees to reduce the monthly repayment by $500 per month. However, his loan term will have to increase so that the bank does not lose out and the interest is still 10% per annum. How long will it take him to repay the loan? (4 marks)

e) After 1 year, on the 1st January 2021, 1 year after taking the bank offer, John decides to take in a housemate for his spare room. With the extra income, John realises he can put an additional $1,000 every month into his loan repayment. Assuming that the interest rate does not change, how long will it take him to repay his loan? (5 marks)

f) As of January 2021, what is his effective interest rate? (3 marks)