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Sec 4 E Maths: Percentage, Interest and Money, practice questions & worked solutions

Percentage, interest and money questions selected from 2023 to 2025 Singapore school E Maths prelim papers, each with the school’s full worked solution.

10 questionsStep-by-step solutionsFree to access

About this topic & key methods

Percentages start in Sec 1, and Sec 3 and Sec 4 E Maths add simple and compound interest, hire purchase, exchange rates, tax and other money problems. Most questions here are short Paper 1 items, with two Paper 2 questions that combine interest, exchange rates and fees.

Attempt each question on paper before opening its worked solution. The solutions are the schools’ own marking schemes, so some steps are brief.

Key methods for percentage and interest

For a reverse percentage, divide by the multiplier: a price after 9% GST is $1.09\times$ the price before
Chain multipliers for successive changes, such as $1.1\times1.09$ for service charge then GST
Simple interest $I=\dfrac{PRT}{100}$
Compound interest $A=P\left(1+\dfrac{r}{100}\right)^n$ ; for monthly compounding use $\dfrac{r}{12}$ and $12n$ periods
To find a growth rate, solve $\left(1+\dfrac{r}{100}\right)^n=\dfrac{A}{P}$ with an $n$ th root
Hire purchase: total paid = deposit + instalments; interest = total paid minus cash price
To compare exchange rates, convert the same amount both ways and compare the results

For lessons that build these methods week by week, see our E Maths tuition for Sec 3 and Sec 4.

Percentage, Interest and Money questions with worked solutions

Unless the question specifies otherwise, give non-exact answers to 3 significant figures and angles in degrees to 1 decimal place.

Q1St Joseph’s Institution2024Prelim P1 Q6●○○ Foundational2 marks

Discount that cancels a markup, St Joseph’s Institution, 2024 Prelim P1 Q6

The marked price of a smart watch at a shop is 25% above the cost price.
The shop gives a $p\,\%$ discount during a sale.

Calculate the value of $p$ such that the shop makes neither a loss nor a profit from the sale of the smart watch. [2]

Show worked solution▾

Let $x$ be the cost price.

$\begin{aligned}1.25x\left(1-\dfrac p{100}\right)&=x\\[4pt]1-\dfrac p{100}&=\dfrac1{1.25}\\[4pt]\dfrac p{100}&=\dfrac15\\[4pt]p&=20\end{aligned}$

Answer: $p=20$

Q2Ahmad Ibrahim Secondary School2025Prelim P1 Q3●○○ Foundational3 marks

Salary plus commission, Ahmad Ibrahim Secondary School, 2025 Prelim P1 Q3

A salesperson earns a fixed weekly salary of $1000 plus 8% commission on the total value of items he sells.

In one week, he sold items worth $1750.
Calculate the total amount the salesperson earned that week. [1]
The following week, the salesperson earned a total of $1450.
Calculate the total value of items he sold that week. [2]

Show worked solution▾

(a)

$\begin{aligned}\text{Total amount}&=\$1000+\frac8{100}\times1750\\&=\$1140\end{aligned}$

(b)

$\begin{aligned}\text{Commission}&=\$1450-\$1000\\&=\$450\end{aligned}$

8% represents $450

$\begin{aligned}100\%\text{ represents }&\$\frac{450}8\times100\\&=\$5625\end{aligned}$

Answer: (a) $1140 (b) $5625

Q3CHIJ St. Nicholas Girls’ School2023Prelim P1 Q12●○○ Foundational3 marks

Percentage more and less, written as a ratio, CHIJ St. Nicholas Girls’ School, 2023 Prelim P1 Q12

John, Eric and Kate walk from point $A$ to point $B$ along the same route.

Eric takes 10 minutes 30 seconds to complete this journey.
John takes 10% less than the time taken by Eric.
Kate takes 20% more than the time taken by Eric.

Calculate the time taken by Kate in seconds. [1]
Express the ratio of the times taken by John, Eric and Kate in the form $a:b:c$ , where $a$ , $b$ and $c$ are integers in their lowest terms. [2]

Show worked solution▾

(a)

$\begin{aligned}\text{Kate's time}&=1.2\times630\text{ seconds}\\&=756\text{ seconds}\end{aligned}$

(b)

$\begin{aligned}\text{John's time}&=0.9\times630\text{ seconds}\\&=567\text{ seconds}\\567:630:756&\\&=9:10:12\end{aligned}$

John, Eric and Kate

$\begin{aligned}&=90\%:100\%:120\%\\&=9:10:12\end{aligned}$

Answer: (a) 756 seconds (b) $9:10:12$

Q4Tanjong Katong Girls’ School2025Prelim P1 Q3●●○ Standard2 marks

Reverse percentage with service charge and GST, Tanjong Katong Girls’ School, 2025 Prelim P1 Q3

Mr Tan had lunch with his friends at a restaurant to celebrate his birthday.

They ordered a meal from a set menu at a special price of $ $x$ .

In addition, they ordered some dishes from the a la carte menu at $96. All dishes from the a la carte menu would be entitled to 20% birthday discount.

After adding 10% service charge and 9% goods and service tax (GST), they paid $257.55

Find $x$ , correct to the nearest whole number. [2]

Show worked solution▾

$(x+96\times0.8)\times1.1\times1.09=257.55$

$x=138\text{ (nearest whole number)}$

Answer: $x=138$

Q5Hua Yi Secondary School2024Prelim P1 Q5●●○ Standard3 marks

Monthly growth rate from compound growth, Hua Yi Secondary School, 2024 Prelim P1 Q5

In a greenhouse, the estimated number of flowering plants increased from 4100 in January 2024 to 4980 in June 2024. The number increased by $c\%$ every month.

Find the value of $c$ . [3]

Show worked solution▾

$\begin{aligned}4980&=P\left(1+\frac r{100}\right)^n\\4980&=4100(1+0.01c)^5\\\sqrt[5]{\frac{249}{205}}&=1+0.01c\\c&=\frac{\sqrt[5]{\frac{249}{205}}-1}{0.01}\\&=3.965=3.97\text{ (3 s.f.)}\end{aligned}$

Answer: $c=3.97$

Q6Bukit View Secondary School2024Prelim P1 Q11●●○ Standard3 marks

Difference between compound and simple interest, Bukit View Secondary School, 2024 Prelim P1 Q11

The difference between simple interest and compound interest for a period of 3 years at 5% per annum is $366.

Find the principal amount. [3]

Show worked solution▾

Interest (compound int) $-$ Simple interest $=366$

$\left[P\left(1+\frac5{100}\right)^3-P\right]-\frac{P\times5\times3}{100}=366$

$\left[1.157625P-P\right]-0.15P=366$

$0.007625P=366$

$P=48000$

Answer: $48 000

Q7Broadrick Secondary School2024Prelim P1 Q9●●○ Standard3 marks

Comparing exchange rates in two countries, Broadrick Secondary School, 2024 Prelim P1 Q9

Keila travels from Singapore to Japan.
She wants to change 850 Singapore dollars ($) into Yen (¥).

The exchange rate in Singapore is $100 = ¥11600 and the exchange rate in Japan is ¥1 = $0.0086.
She claims that she will receive more if she changes the money in Singapore.
Justify if her claim is true.
Show your working. [3]

Show worked solution▾

In Singapore:

$\text{Amount of Yen}=\frac{850}{100}\times11600=98600$

In Japan:

$\text{Amount of Yen}=\frac{850}{0.0086}\times1=98837.21$

$98837.21>98600$

Her claim is not true. She will receive (237.21 Yen) more if she changes in Japan.

Answer: Her claim is not true. She will receive ( $237.21$ Yen) more if she changes in Japan.

Q8Yio Chu Kang Secondary School2025Prelim P1 Q20●●○ Standard4 marks

Hire purchase deposit and flat interest rate, Yio Chu Kang Secondary School, 2025 Prelim P1 Q20

The cash price of a laptop is $1800.
The hire-purchase price of the laptop is $1944.
The hire-purchase price is a deposit plus 24 equal monthly payments of $66.

Calculate the amount of deposit to be paid. [2]
Calculate the interest rate per annum. [2]

Show worked solution▾

(a)

$\begin{aligned}1944&=D+66\times24\\D&=1944-1584\\&=\$360\end{aligned}$

(b)

Int:

$1944-1800=\frac{(1800-360)(R)(2)}{100}$

$R=\frac{144\times100}{1440\times2}=5$

Answer: (a)$360 (b)5%

Q9Presbyterian High School2025Prelim P2 Q2●●● Challenging9 marks

Simple interest, compounding frequency and exchange rates, Presbyterian High School, 2025 Prelim P2 Q2

Linus invests a sum of money at 7% per annum simple interest. At the end of $n$ years, the amount is more than twice the initial sum of money. Find the minimum integer value of $n$ . [3]
Marcus wants to invest $12,000 for 4 years and is exploring two investment options with different compounding frequencies.
Determine which option Marcus should choose. Justify your reasons with calculations. [3]
A group of students travelled to Malaysia. They exchanged Singapore dollars (SGD) to Malaysian ringgit (MYR) at a rate of SGD 1 = MYR 3.20.
They spent MYR 2525 on accommodation and food. They also bought 80 litres of fuel at MYR 2.50 per litre. They exchanged the remaining MYR at a rate of SGD 1 = MYR 3.25 and received SGD 60.
Calculate the amount of SGD they exchanged at the start of their trip. [3]

Show worked solution▾

(a)

Let the principal be $P$

Total amount $=Prt+P$

After $n$ years

$\begin{aligned}\text{Amount}&=P\left(1+\frac{7n}{100}\right)\\P\left(1+\frac{7n}{100}\right)&>2P\\\left(1+\frac{7n}{100}\right)&>2\\0.07n&>1\\n&>14.285\\n&=15\end{aligned}$

$\begin{aligned}\frac{Prn}{100}&>P\\rn&>100\\7n&>100\\n&>14.2857\\n&=15\end{aligned}$

(b)

Option A

$\begin{aligned}12000\left(1+\frac{0.065}{12}\right)^{12\times4}\\=\$15552.25\end{aligned}$

Option B

$\begin{aligned}12000\left(1+\frac{0.068}2\right)^{2\times4}\\=\$15679.98\end{aligned}$

Answer: Option B

(c)

$\begin{aligned}\text{Fuel cost}\\&=80\times2.50\\&=200\text{ MYR}\\\text{Total Spending}\\&=2525+200+(3.25\times60)\\&=2920\text{ MYR}\\\text{Initial SGD}\\&=2920\div3.20\\&=912.50\text{ SGD}\end{aligned}$

Answer: (a) $n=15$ (b) Option B (c) SGD 912.50

Q10Fairfield Methodist School (Secondary)2023Prelim P2 Q2●●● Challenging9 marks

CPF, fuel cost, a changing interest rate and card fees, Fairfield Methodist School (Secondary), 2023 Prelim P2 Q2

Jeremy earns $7500 each month.
Jeremy contributes 20% of his first $6000 into his CPF funds.
21% of his CPF funds are distributed to Medi-Save account.
16% of his CPF funds are distributed to Special account.
The remaining of his CPF funds are distributed to Ordinary account.
Calculate the amount of Jeremy's CPF that is distributed to Ordinary account. [2]
Jeremy drives a car that consumes 12.5 litres of petrol for every 100 km.
The cost of petrol is $2.50 per litre and there is an additional petrol levy of 20 cents for every litre.
Jeremy drives 440 km to a town in Malaysia.
Calculate the cost of the petrol used for this journey. [2]
Jeremy invested $10 000 of his savings for 2 years. The interest from his investment is deposited back to his investment account at the end of each year. The rate of interest for the first year is 2.5%. At the end of the second year, the overall percentage increase of his investment is 8.65%.
Find the rate of interest for the second year. [2]
Jeremy is in Japan and decides to buy a jacket for ¥50 000 using a credit card.
The cashier offers him 2 options to pay for the jacket;
- Option A: pay in Singapore dollars ($) $468.16 or
- Option B: pay in Japanese yen (¥) ¥50 000.
When paying in Japanese yen, the credit card company will convert the amount to Singapore dollars and there is a currency conversion fee of 1.5%.
The exchange rate between Singapore dollars and Japanese yen is $1 = ¥108.
Which option should Jeremy choose? Show your working clearly. [3]

Show worked solution▾

(a)

CPF funds

$\begin{aligned}0.20\times6000&=\$1200\end{aligned}$

Ordinary Account

$\begin{aligned}63\%\times1200&=\$756\end{aligned}$

(b)

Amount Petrol used

$\begin{aligned}4.4\times12.5&=55\,l\end{aligned}$

Petro Cost

$\begin{aligned}55\times2.70&=\$148.50\end{aligned}$

(c)

Return after 1 $^{\text{st}}$ yr

$\begin{aligned}&0.025\times10000\\&=\$250\end{aligned}$

Return after 2 $^{\text{nd}}$ yr

$\begin{aligned}&0.0865\times10000-250\\&=\$615\end{aligned}$

Let $x\,\%$ be rate of interest for 2 $^{\text{nd}}$ year

$\begin{aligned}\frac{10250x}{100}&=615\\x&=6\end{aligned}$

(d)

Option B

$\begin{aligned}&1.015\left(\frac{50000}{108}\right)\\&=\$469.907\\&=\$469.91\ (\text{2dp})\end{aligned}$

Option A because the total charge for Option B is higher than Option A

Answer: (a) $756 (b) $148.50 (c) $6\%$ (d) Option A

Need help with percentage and interest? Our Sec 4 E Maths tuition classes work through prelim questions like these every week.

More practice related to percentage and interest

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Sec 4 E Maths: Ratio, Proportion, Speed and Map Scales

Sec 4 E Maths: Prime Factors, HCF, LCM and Approximation

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