Year 9 Maths The Thai Guy

Lesson 14.3 · 30 min

Percentage Change and Compound Interest

Using multipliers for percentage increases and decreases, simple versus compound interest, and repeated percentage change.

In this lesson you will learn to…

  • Use a multiplier to increase or decrease by a percentage
  • Calculate simple interest
  • Calculate compound interest and repeated percentage change using powers
  • Explain why two successive changes of do not simply add

Why this matters

Savings accounts, loans, credit cards, inflation and the value of a new car all change by a percentage each year. Compound change is how money grows — and how debt grows too.

Why compound beats simple

With simple interest you earn interest only on what you put in. With compound interest you also earn interest on your interest. Over a few years the difference is small; over 30 years it is enormous.

Jamil’s mistake

In a sale, prices are cut by 25%, then by a further 25%. Jamil says items are now half price. For a 100-dollar coat: 100×0.75=75100 \times 0.75 = 75, then 75×0.75=56.2575 \times 0.75 = 56.25. The second 25% is taken off a smaller price, so the total reduction is only 43.75%.

Likewise, increasing a 400-dollar coat by 20% and then decreasing by 20% does not bring it back: 400×1.2×0.8=384400 \times 1.2 \times 0.8 = 384.

Calculator tip. Use the power key: 400×1.035400 \times 1.03^5 is faster and more accurate than five separate multiplications.

Key rules and formulas

  • Multipliers

    An increase of 15% leaves you with 115% of the original. A decrease of 12% leaves 88%.

  • Simple interest

    The same interest is paid every year: is the principal, the rate per year and the number of years.

  • Compound interest

    Interest is added each year, so the next year's interest is worked out on a bigger amount. Do not round until the end. Subtract the principal to find the interest.

  • Changes multiply, they do not add

    Reducing by 25% twice is — a 43.75% reduction, not 50%.

Worked examples

Worked example 1

Increase and decrease

A bed costs 540 dollars before 15% sales tax. A car costing 8400 dollars has a 12% discount. Find each final price.

Try it yourself first, then reveal the solution one step at a time.

Worked example 2

Simple against compound

Rahul invests 400 dollars for 5 years. Compare 3.1% simple interest with 3% compound interest.

Try it yourself first, then reveal the solution one step at a time.

Worked example 3

Depreciation

A car bought for 13 000 dollars loses 12% of its value each year. What is it worth after 2 years?

Try it yourself first, then reveal the solution one step at a time.

Practice: percentage change and interest

11 questions

Eleven questions. A calculator is fine. Give money to the nearest cent.
  1. Question 1 of 11Match the pairsFoundation
    Match each change to its multiplier.

    Pick an answer, then choose the row it belongs to. You can also drag it.

    • Increase by 15%
    • Decrease by 12%
    • Increase by 3%
    • Decrease by 5%
    • Increase by 100%

  2. Question 2 of 11Type the answer
    A bed costs 540 dollars. 15% sales tax is added. What is the final price?
    dollars
  3. Question 3 of 11Type the answer
    Find the simple interest on a loan of 40 000 dollars at 8% per year for 5 years.
    dollars
  4. Question 4 of 11Complete the table
    Find the simple interest on each loan.
    LoanRate per yearYearsInterest (dollars)
    20015%4
    100015%2
    300012%2
    45009%3
  5. Question 5 of 11Type the answer
    Francesca invests 2000 dollars at 1.8% compound interest. How much interest has she earned after 5 years?
    dollars
  6. Question 6 of 11Step by step
    Work year by year.
    Rahul invests 400 dollars at 3% compound interest.
    1. Value after 1 year:
      dollars

  7. Question 7 of 11Type the answer
    A car bought for 13 000 dollars loses 12% of its value each year. Find its value after 3 years, to the nearest dollar.
    dollars
  8. Question 8 of 11Multiple choice
    Sale prices are cut by 25%, then by a further 25%. Jamil says everything is now half price. Which is true?
  9. Question 9 of 11Type the answer
    A ball is dropped from 4 m. Each bounce it rises to 70% of the height it fell from. How high does it rise after 3 bounces, to the nearest cm?
    cm
  10. Question 10 of 11Choose all that applyChallenge
    One million bacteria increase by 10% each hour. Select every true statement.

    Select every correct answer — there may be more than one.

  11. Question 11 of 11Type the answer
    A share increases by 2% one year and 3% the next. What is the overall percentage increase?
    %