A fund is started at $\$6000$ and compound interest of $3\%$ is added to the fund at the end of each

Question

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] 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 [2] If the fund is fully withdrawn at the beginning of sixteenth year, find the least value of $k$ to the nearest integer. [2]

Accepted Answer

(i) 19th year; (ii) $$503$

2017 JJC P1 Q4

2017 JJC P1 Q4

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