2017 JJC P1 Q4

A fund is started at \(\$6000\) and compound interest of \(3\%\) is added to the fund at the end of each year. If withdrawals of \(\$k\) are made at the beginning of each of the subsequent years, show that the amount in the fund at the beginning of the \(\left( n+1 \right)\)th year is

\(\mathrm{}\!\!\$\!\!\mathrm{}\frac{100}{3}\left[\left(180-k\right){{\left(1.03\right)}^{n}}+k\right]\).[5]

1. It is given that \(k=400\). At the beginning of which year, for the first time, will the amount in the fund be less than \(\$1000\)?[2]
2. If the fund is fully withdrawn at the beginning of sixteenth year, find the least value of \(k\) to the nearest integer.[2]