Simple Interest

1Summary 重點摘要

Learn simple interest calculation, know how much interest you get when saving money in bank.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: The simple interest formulaThe basic formula for simple interest is I = P × r × t, where I is the interest, P the principal, r the annual interest rate as a decimal, and t the number of years. Why is it called simple? Because each period's interest is computed on the original principal only; earlier interest is not added to the principal, so the yearly interest stays the same. For example, a principal of 1000 at 5% earns 50 each year. A common mistake is substituting the percentage directly without converting it to a decimal.
2. Step 2: Applying the formulaWhen applying the formula, write down each quantity first, then substitute. For example, 1000 is deposited at an annual rate of 5% for 3 years: I = 1000 × 0.05 × 3 = 150, so the interest after three years is 150. Why write the working rather than compute mentally? The written form shows how P, r and t correspond, prevents confusion when numbers grow, and exam marking requires clear steps. A common mistake is getting the unit of t wrong, treating 3 months as 3 years and inflating the interest twelvefold.
3. Step 3: The amountThe amount is the total received at the end, equal to principal plus interest: A = P + I. In the example above, the amount = 1000 + 150 = 1150, so 1150 is received after three years. Why distinguish interest from amount? When the question asks for the interest, answer with I only; only when it asks for the total should A be given, and mixing them answers the wrong question. A common mistake is answering with the amount when the interest was asked, or forgetting to add the interest back to the principal.
4. Step 4: Convert time to yearsThe t in the formula must be in years; if the time is given in months, divide by 12 first. For example, 6 months means t = 612 = 0.5 years, 9 months means t = 912 = 0.75 years, and 2 years 3 months means t = 2.25 years. Why convert? Because r is an annual rate matched to one year of time, and mismatched units break the formula. A common mistake is substituting the number of months directly, treating 6 months as 6 years and inflating the interest twelvefold; unify the units before answering.
5. Step 5: Convert the rate to a decimalAnnual rates are usually percentages and must be converted to decimals before substitution by dividing by 100. For example 5% means r = 0.05, 8% means r = 0.08, and 12.5% means r = 0.125. Why? Because 5% mathematically means 5100 = 0.05, and the formula needs this ratio. A common mistake is substituting 5 directly, making the interest a hundred times too large, such as 1000 × 5 × 3 = 15000, which is clearly unreasonable; after answering, check that the interest is proportionate to the principal.
6. Step 6: A complete exampleCombine all the points: someone borrows 5000 at an annual rate of 8% for 2 years; find the interest payable. Convert the rate first: r = 8% = 0.08; then apply the formula: I = 5000 × 0.08 × 2 = 800, so the interest payable is 800; the amount = 5000 + 800 = 5800, which is repaid in total. Why does the order matter? Listing the known values, converting the units, then substituting prevents missing steps. A common mistake is answering with the interest when the amount was asked; underline what the question requires.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Formula: I = P × r × t
• P = Principal
• r = Annual rate (decimal)
• t = Years
• Amount = Principal + Interest