GP Calculus

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Muthu started working at a company on 1 January 2002 with an initial annual salary of RM18,000. Every January, the company increased his salary by 5% of the previous year's salary. Calculate
a)his annual salary, to the nearest RM, for the year 2007.
b)the minimum value of n such that his annual salary in the nth year will exceed RM36,000.
c)the total salary, to the nearest RM, paid to him by the company, for the years 2002 to 2007.

• GP Calculus -

a) 18000 * 1.05^5
b) 36000 = 18000 * 1.05^n
n = ln 2/ln 1.05

c) sum of first n terms of a GP is
a(1-r^n)/(1-r) = 18000(1-1.05^6)/(1-1.05)

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