2026 CCHMS P2 Q2

Secondary 4

12 marks

Mei invests a sum of money at a compound interest of $r\%$ per annum.
At the end of 4 years, the value of her investment has increased by 25%.
Find the value of $r$.[3]
John borrows $\$15\,000$ from a Singapore bank for 3 years to pay for an overseas course in France that costs €9800.
The exchange rate between Singapore dollars and euros is $\$1$ = €0.625.
The bank charges simple interest at a rate of 5% per annum.
1. Show with clear working whether the amount borrowed is sufficient to pay for the course fee.[1]
2. Calculate the total amount John has to repay the Singapore bank.[2]
In a number sequence, the sum of the first $n$ terms is given by $S_n=n^2+3n$.
1. Find the sum of the 15th to the 30th terms.[1]
2. By finding $S_{n-1}$, show that all the terms in the number sequence are always even.[3]
3. $T_3,T_6,T_9,\ldots$ is a new sequence formed by taking every 3rd term of the original sequence.
  Find an expression, in terms of $m$, to represent the $m$th term of the new sequence.[2]

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Answer:(a) $5.74$ (b)(i) Insufficient: €9375 < €9800. (ii) $\$17\,250$. (c)(i) $752$ (ii) $S_{n-1}=n^2+n-2$, $T_n=2(n+1)$ is even. (iii) $6m+2$.

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