Interest

1Summary 重點摘要

Learn how to calculate simple interest — principal × rate × time, three numbers and done.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Know the three basic numbersTo calculate interest, you need three things: principal, interest rate, and time. Principal is how much you originally deposit; rate is the percentage per period; time is how long. Example: Deposit $1000, annual rate 5%, for 2 years. Rates are usually quoted per year: an annual rate of 5% means each full year earns 5% of the principal, i.e. 1000 × 5% = $50. Only when principal, rate and time are all known can the calculation begin.
2. Step 2: Simple interest formulaSimple interest formula: Interest = Principal × Rate × Time. Written as I = P × R × T. This is the basic formula used for all simple interest questions. Example: I = 1000 × 5% × 2 = 1000 × 0.05 × 2 = $100. Convert the percentage to a decimal before substituting: 5% = 0.05. Check with 'interest per year × years': 1000 × 0.05 = $50 and 50 × 2 = $100, agreeing with the formula.
3. Step 3: Calculate amountAmount is total you get back at maturity: Amount = Principal + Interest. Example: $1000 + $100 = $1100. Remember: amount includes both principal and interest, not just interest! For example, at 4% p.a. on $2500 for 3 years: interest = 2500 × 0.04 × 3 = $300, and amount = 2500 + 300 = $2800. 'How much in total can be received' asks for the amount; only 'how much interest' wants the interest alone.
4. Step 4: Units must match!Key point! Rate and time units must match. If rate is annual, time must be in years. If you deposit for 6 months, write it as 0.5 years, not 6! Example: Annual rate 5%, 6 months, interest = 1000 × 0.05 × 0.5 = $25. Likewise, a quarterly rate pairs with the number of quarters and a monthly rate with the months; useful conversions are 18 months = 1.5 years and 90 days = 0.25 year (on a 360-day year).
5. Step 5: Reverse calculate anythingFrom formula I = P × R × T, knowing any three lets you find the fourth. Find principal: P = I ÷ (R × T). Find rate: R = I ÷ (P × T). Find time: T = I ÷ (P × R). Example: Interest $100, annual rate 5%, principal $1000, time = 100 ÷ (1000 × 0.05) = 2 years. Watch unit consistency when reversing too; as a check, substitute principal, rate, time and interest back into the formula together and see that they agree.
6. Step 6: Check if simple or compoundSecondary school teaches simple interest, meaning interest doesn't earn interest. For compound interest, interest is added to principal to earn more interest — the number is different. DSE covers compound interest; S2 and S3 only simple interest. If question says 'simple interest', use I = PRT. The gap widens with time: on the same $1000 at 5% p.a., simple interest for two years is $100 in all, while compound interest charges the second year on $1050, giving $102.5 for the two years — $2.5 more.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Simple interest: I = P × R × T
• Amount = Principal + Interest
• Rate and time units must match
• Divide percentage by 100 before multiplying
• S2/S3 is simple interest, not compound