2013 ACJC Promo Q15

A man met with an accident and went into a coma on 10\(^{\mathrm{th}}\) January 2013. As a result, he did not pay the bank the outstanding balance of \(\$M\) for his credit card bill when it is due for payment on 27\(^{\mathrm{th}}\) January 2013. On the 27\(^{\mathrm{th}}\) of each month when the payment for the credit card bill is due, the bank will charge a 2% interest on any outstanding balance what is unpaid. After the 2% interest has been added, the bank will still charge an additional late payment charge of \(\$L\) monthly.

1. Express in terms of \(L\) and \(M\), his outstanding balance on his credit card on 1\(^{\mathrm{st}}\) February 2013.[1]
2. If the man still remains in coma exactly \(n\) months later on the day he met with an accident, show that the accumulated outstanding balance on the man’s credit card is \({{1.02}^{n}}M+50L\left( {{1.02}^{n}}-1 \right)\).[3]
3. Given that \(M=1000\) and \(L=55\). Find the least value of \(n\) when the accumulated outstanding balance on his credit card first exceeds \(\$2010\).[2]