A company predicts a yearly profit of $\$100\;000$ in the year 2013. The company also predicts tha

Question

A company predicts a yearly profit of $\$100\;000$ in the year 2013. The company also predicts that the yearly profit will rise each year by $5\%$. Show that the predicted profit in 2015 is $\$110\;250$.[1] Find the first year in which the yearly predicted profit exceeds $\$200\;000$.[3] Find, in terms of $m$, the sum of the predicted yearly profits from the year 2015 till the year $\left( 2000+m \right)$, where $m>15$.[2] An arithmetic progression has first term $a$ and common difference $d$, where $a$ and $d$ are non- zero. The second, seventh and ninth terms of the arithmetic progression are consecutive terms of a geometric progression. Find, in terms of $d$, the sum of the first 20 odd-numbered terms of the arithmetic progression.[4]

Accepted Answer

(i) $110250$; (ii) 2028; (iii) $2205000(1.05^{m-14}-1)$; (iv) $\frac{580}{3}d$

2013 IJC P2 Q2

2013 IJC P2 Q2

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