Compound Interest and Repeated Percentage Change · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

The multiplier does the repeating

Mathematics · Ratio & Proportion · ages 14-15
Name ______________________   Date ____________

  1. You put £500 in an account paying 5 percent compound interest per year. How much is there after 2 years, in pounds?

    Answer: ______________

  2. You put 500 pounds in an account paying 5 percent compound interest per year. How much is there after 2 years, in pounds?

    Answer: ______________

  3. A price falls by 20 percent. Which multiplier gives the new price?

    • 0.8
    • 1.2
    • 0.2

  4. A savings rate rises by 12 percent. Which multiplier turns an old balance into the new one?

    • 0.12
    • 1.12
    • 1.2

  5. Sam banks 100 pounds. It grows 10 percent one week, then shrinks 10 percent the next. Why does it end below 100?

    • Banks round down
    • The shrink applies to 110, which is more than the growth applied to
    • Percentages always destroy money

  6. You invest £400 at 10 percent compound interest per year. What is it worth after 3 years, in pounds?

    Answer: ______________

  7. A jacket costs £200. Its price rises by 10 percent, then falls by 10 percent. What is the final price?

    • £198
    • £200
    • £202
    • £180

  8. A jacket costs 200 pounds. Its price rises 10 percent, then falls 10 percent. What is the final price?

    • 200 pounds
    • 202 pounds
    • 198 pounds

  9. You invest 400 pounds at 10 percent compound interest per year. What is it worth after 3 years, in pounds?

    Answer: ______________

  10. Two savers deposit the same sum at the same rate, but Ana starts five years earlier. Why does she finish far ahead?

    • Early pounds compound through extra powers of the multiplier
    • Banks reward early risers with gifts
    • Simple interest favours the young
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Answer key

For grown-ups. Fold this page away before handing over the rest.

The multiplier does the repeating W1-mt_2vJz9VKle_-s1

  1. 551.25 · A 5 percent rise is a multiplier of 1.05, and two years means squaring it: 500 x 1.1025 = 551.25.
  2. 551.25 · A 5 percent rise is 1.05, squared for two years: 500 times 1.1025.
  3. 0.8 · One minus 0.2 keeps the 80 percent that remains.
  4. 1.12 · One plus 0.12 keeps the whole balance and adds the rise.
  5. The shrink applies to 110, which is more than the growth applied to · Ten percent of 110 beats ten percent of 100, so the loss wins.
  6. 532.4 · The multiplier is 1.1 and three years means cubing it: 400 x 1.331 = 532.4.
  7. £198 · The rise gives £220, and the 10 percent fall is taken from £220, leaving £198, which is below the start.
  8. 198 pounds · The rise gives 220, and the fall is taken from 220, leaving 198.
  9. 532.4 · Three years means cubing 1.1: 400 times 1.331 is 532.4.
  10. Early pounds compound through extra powers of the multiplier · Extra years mean extra multiplications, and the gap explodes.
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