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**Punch** Mrs Wong retired in 2006, she put a sum of $5000 into a fund that has a constant rate of return of 5 % per annum. Starting in 2006, she withdraws $400 each year and gives the money to her granddaughter as a birthday gift.

a) Denote the amount of money Mrs Wong has at time t years by $x.

b) In which year will the granddaughter receive her last $400?

a) x$\displaystyle =5000+\frac{(5000)(1-0.05^t)}{1-0.05}-400t $

b) In the year granddaughter receives last $400, $\displaystyle x<400$

$\displaystyle 5000+\frac{(5000)(1-0.05^t)}{1-0.05}-400t<400$