All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
$\frac{n}{2} [2(100) + 10(n-1)] > 5000$

Using the graphing calculator, smallest n = 24.

Thus, Mrs A’s account will have more than $5000 on 1 December 2002. (ii) Amount at the end of 1st month $= 100 \times 1.005$ Amount at the end of 2nd month $= (100 \times 1.005 + 100) \times 1.005 = 100 \times 1.005^2 + 100 \times 1.005$ Amount at the end of nth month $= 100 \times 1.005^n + \ldots 100 \times 1.005$ $= 20100 (1.005^n - 1)$ Mr B’s account will be more than$5000 on September 2004.

(iii)
$100x \frac{x^{35} - 1}{x-1} + 100 = 5000$

Using Graphing Calculator, $x = 1.01796$

Thus the interest rate is 1.80% per month.