Sequence and Series - Problems involving inequalities

In January 2025, Samantha obtained a housing loan of \(\$600\;000\) from the National Housing Trust (NHT), which applies an annual interest rate of \(3\%\) at the end of each year. Every middle of the month, starting from January 2025, Samantha begins repaying an instalment of \(\$4500\).

1. Demonstrate that the amount Samantha owes NHT at the start of the \(n\) year can be expressed as \(1,854,000 - 1,254,000(1.03)^{n-1}\).
2. Determine the earliest month and year in which she will fully repay her loan and the amount of her final instalment.
3. Calculate the total interest she will have paid upon completing the loan repayment.