2021 TJC P1 Q6

The sum of the first \(5\) terms of an arithmetic series is \(\frac{1}{3}\) times the sum of its next \(5\) terms. Given that the common difference of this series is \(3\), find the first term of the series.[4]

A teacher makes an initial payment of \(\$\,k\) to a retirement fund on 1 January 2021, and thereafter, she contributes \(\mathrm{ }\!\!\$\!\!\mathrm{}\,\,\mathrm{12000}\) per year to it on the first day of each year. The retirement fund guarantees a compound annual interest rate of \(4\%\) on the last day of the year.