2013 AJC P1 Q6(b)

Mr Wee borrowed \(\$3400\) from an unlicensed money lender on 1st June 2013. The amount he owes the lender at the beginning of each month is twice the outstanding amount at the end of the previous month.

From the month of August 2013, Mr Wee decided to repay \(\$7000\) in the middle of each month.

Find, in terms of \(n\), the outstanding amount owed at the end of the \(n\)th month.

Hence find the earliest month when he has fully repaid his loan.[5]