Mr Chan’s monthly pay for the first quarter of the year (i.e. first three months) is $\$3000$. For

Question

Mr Chan’s monthly pay for the first quarter of the year (i.e. first three months) is $\$3000$. For the second quarter monthly pay, he gets an increment of $60\%$ of his first quarter monthly pay. Subsequently, from the third quarter onwards, he gets an increment of $60\%$ of his previous increment every quarter. ${{Q}_{n}}$ denotes his monthly pay for the ${{n}^{\mathrm{th}}}$ quarter, where $n\ge 1$. Prove that ${{Q}_{n}}=7500\left( 1-{{0.6}^{n}} \right)$.[3] Find to the nearest dollar, his pay for his $17\mathrm{th}$ month of work.[1] Find to the nearest dollar, his total salary for the first two years of work.[2] Mr Chan decides to quit his job when his increment is less that $\$80$. How many months will he stay in this job?[1] Mr Chan’s company is planning to implement a loyalty incentive scheme to retain workers with relevant skills and experience. $10$ chosen workers will receive a loyalty incentive of $\$90$ in their pay every month. This monthly loyalty incentive will increase by $\$40$ every year. The company sets aside a budget of $\$200\,000$ for this scheme. what is the maximum number of years for which this scheme can be implemented with this budget?[2] what is the highest loyalty incentive amount Mr Chan can hope to receive if he is selected for this scheme?[1]

Accepted Answer

(a)(i) $Q_n=7500(1-0.6^n)$ (ii) $\text{SGD }7150$ (iii) $\text{SGD }146817$ (iv) $24$ months (b)(i) $7$ years (ii) $\text{SGD }330$ in the seventh year

2022 ACJC P1 Q9

2022 ACJC P1 Q9

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