Every receipt, phone bill, savings account statement and money changer board in Singapore is built from the same few calculations: percentages, interest and exchange rates. These are a guaranteed part of the Sec 3–4 G1 Maths exam, so mastering a small set of methods earns reliable marks.
Two ground rules run through every section. Work in Singapore dollars and round final money answers to the nearest cent (2 decimal places), only at the end. Find x% of an amount as amount × x ÷ 100.
What these notes cover
- •Percentage of an amount
- •Profit and loss
- •Discount
- •GST at 9%
- •Discount first, then GST
- •Simple interest
- •Compound interest
- •Hire purchase and instalment plans
- •Utilities: reading an SP Group bill
- •Income tax
- •Money exchange
- •Common mistakes and exam technique
Key definitions
- Cost price and selling price
- The cost price (CP) is the amount the seller paid for an item. The selling price (SP) is the amount it is sold for. If SP is higher than CP the seller makes a profit, and if SP is lower the seller makes a loss.
- Simple interest
- Interest paid only on the original amount deposited (the principal). The interest is the same every year and never grows.
- Compound interest
- Interest that is added to the principal each year, so the next year's interest is worked out on a bigger amount and the interest itself gets bigger every year.
- Instalment plan (hire purchase)
- A way to take an expensive item home now and pay in parts: a deposit up front, then a fixed monthly instalment for a set number of months. It normally costs more than the cash price.
- Chargeable income
- Gross income minus reliefs, which are amounts the government lets you subtract, for example for supporting parents or CPF contributions. Only chargeable income is taxed.
Key formulas
Percentage change in price
Profit = SP − CP and loss = CP − SP. The original price is the cost price, so always divide by the cost price, never the selling price.
Sale price after a percentage discount
A percentage discount is always taken of the marked price. A 25% discount means you pay 75%, so multiply by 0.75. Discount = marked price − sale price.
Adding and removing 9% GST
A GST-inclusive price is 109% of the original, so divide by 1.09 to remove GST. In a shop, the discount comes off the marked price first and GST is then charged on the discounted price.
Simple interest
P = principal ($), R = rate per year as a percentage (write 1.8% as 1.8), T = time in years (8 months = 8 ÷ 12 years), I = interest only. Total amount = P + I.
Compound interest
P = principal, r = rate per year as a percentage, n = number of years, A = total amount (principal plus interest). The formula is printed on the exam paper. Interest earned = A − P.
Instalment plan
total paid = deposit + monthly instalment × number of months
Extra cost of the plan = total paid − cash price. A 2-year plan means 24 months, not 2.
Worked example
Hui Min deposits $5000 into an account paying 1.8% per year compound interest, compounded yearly. Using the formula A = P(1 + r ÷ 100)ⁿ, calculate the total amount after 3 years and the interest she earns.
- 1Identify the values: P = 5000, r = 1.8, n = 3.
- 2Substitute into the formula: A = 5000(1 + 1.8 ÷ 100)³.
- 3Work out the bracket first: 1 + 1.8 ÷ 100 = 1.018.
- 4Apply the power: 1.018³ = 1.054977832. Keep the full calculator display.
- 5Multiply by the principal: 1.054977832 × 5000 = 5274.889…, so A = $5274.89 to the nearest cent.
- 6The question asks for the interest, so subtract the principal: interest = A − P = 5274.89 − 5000 = $274.89.
- 7Simple interest on the same $5000 at 1.8% for 3 years is $270. Compound interest earns $4.89 more because, from Year 2 onwards, interest is calculated on a bigger balance.
Watch out: Stopping at A = $5274.89 loses the final mark. The formula gives the total amount, so subtract P whenever the question asks for the interest earned.
Common mistakes
Removing GST by multiplying by 0.91
Wrong: Taking away 9% of a $109 GST-inclusive bill: 109 × 0.91 = $99.19.
Right: The 9% was charged on the original price, not on the $109 total. The bill is 109% of the original, so divide by 1.09: 109 ÷ 1.09 = $100.
Converting currency in the wrong direction
Wrong: Multiplying in both directions when SGD 1 = MYR 3.30: MYR 500 × 3.30 = 1650, so MYR 500 becomes SGD 1650.
Right: Multiply by 3.30 for SGD → MYR and divide by 3.30 for MYR → SGD: 500 ÷ 3.30 = SGD 151.52. At this rate, the MYR figure should always be the bigger number.
Applying the tax rate to the whole income
Wrong: Taxing all of a $40,000 chargeable income at 3.5%: 0.035 × 40000 = $1,400.
Right: The 3.5% applies only to the portion above $30,000: tax = 200 + 0.035 × 10000 = 200 + 350 = $550. Always subtract reliefs from gross income first.
Questions students ask
How do you calculate the price before GST in Singapore?
A price that includes 9% GST is 109% of the original, so divide by 1.09 to remove the GST. For example, a S$130.80 bill inclusive of GST was S$120.00 before GST. Check by working forwards: 120.00 × 1.09 = 130.80.
What is the difference between simple and compound interest?
Simple interest is paid only on the principal, so it is the same every year: $5000 at 1.8% for 3 years earns $270. With compound interest, each year's interest is added to the principal, so the same deposit earns $274.89. The gap widens the longer the money is left in.
Do I need to memorise the compound interest formula for Sec 3 G1 Maths?
No. The formula A = P(1 + r ÷ 100)ⁿ is printed on the question paper whenever you need it. Copy it out exactly, substitute the values one letter at a time, and subtract P if the question asks for the interest.
How do you work out the total cost of an instalment plan?
Multiply the monthly instalment by the number of months, then add the deposit. For a phone with a $199 deposit and $95 a month for 12 months, the plan costs 199 + 1140 = $1,339, which is $140 more than the $1,199 cash price. Remember that a 2-year plan means 24 months.
In the full PDF
- •Further worked examples: simple interest, discount followed by GST, two-tier income tax, and plan-versus-cash comparisons
- •A mock SP Group utilities bill (electricity in kWh, water in m³) totalled step by step with 9% GST
- •The full six-pitfall checklist, including rounding too early and using the wrong time unit for simple interest
- •Reverse-percentage and size checks for proving GST and currency answers by working forwards
- •Exam technique for protecting method marks, plus a one-page formula sheet and section summaries