Ray and Betty Read wish to borrow $600,000 to buy a home. The loan from Battlers Bank requires equal monthly repayments over 20 years, and carries.an interest rate of 4.8% per annum, compounded monthly. The first repayment is due at the end of the first month.

You are required to calculate:

i) the effective annual interest rate on the above loan.

ii) the amount of the monthly repayment (consisting of interest and principal repayment components) if the same amount is to be repaid every month over the 20 year period of the loan.

iii) the amount of $X, if – instead of the above – Battlers Bank agrees that Ray and Betty will repay the loan by paying the bank $3,300 per month for the first 12 months, then $3,750 a month for the next 12 months, and after that $X per month for the balance of the 20 year term.

iv) how long (in years and months) it would take to repay the loan if, alternatively, Ray and Betty decide to repay $3,500 per month, with the first repayment again being at the end of the first month after taking the loan, and continuing until the loan was repaid.

v) under option iv) above, the amount of the final repayment. [NOTE: Towards the end of the loan repayment period, after the final full monthly instalment of $3,500 is paid, a lesser amount is likely to be outstanding. That amount, plus interest to the end of the following month, is the final loan repayment amount.]