2016 SRJC P1 Q4

Andy and his fiancée signed up for a new \(4\)-room flat in Boon Keng. They take up a housing loan of \(\$450, 000\) provided by BEST bank for the purchase. The couple pay a fixed monthly instalment of \(\$A\) on the first day of each month. A fixed interest rate of \(1.6\%\) is charged on the last day of each year, based on the remaining loan amount at the beginning of that year before the \({{1}^{\mathrm{st}}}\) monthly instalment is paid. If the first instalment is paid in January \(2016\),

1. Show that the amount the couple owe the bank at the end of \(2017\) is \(\$\left[464515.20-24.579A\right]\).[1]
2. Given that \(A\) is \(1500\), find the date and amount of the final repayment to the nearest cent.[5]