2021 HCI Promo Q12

A couple takes up housing loan of \(\$L\) and the interest is charged before each monthly repayments at a fixed rate of \(p\%\) per annum. Their monthly repayment commences on 1 September 2021. Monthly repayments of \(\$x\) are due and payable on the first day of subsequent months until their housing loan is fully repaid.

1. State an expression in terms of \(L\) and \(p\) for the interest charged before their first repayment on 1 September 2021.[1]
2. Show that the outstanding loan at the start of the \({{n}^{\mathrm{th}}}\) month after their monthly repayment is given by
   \({{\left( 1+\frac{p}{1200} \right)}^{n}}L-\frac{1200x}{p}\left[ {{\left( 1+\frac{p}{1200} \right)}^{n}}-1 \right]\).[3]

The couple is taking a housing loan of \(\$504,000\) at a fixed interest rate of \(2.6\%\) per annum.

3. Calculate the monthly repayment if the couple plans to repay the loan in \(30\) years.[2]