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.

KS Comments:

Students should reproduce the table (with its succeeding and preceding values) to substantiate their answers for (i) and (ii). For (i), its necessary to identify the month; just use your fingers to count.

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