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Compound Growth and Decay: Understanding Compound Interest and Depreciation

Learn about compound growth and decay, specifically compound interest and depreciation. Discover how to calculate and interpret results.

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Compound Growth and Decay: Understanding Compound Interest and Depreciation

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  1. What you need to know: The most typical example of compound growth is compound interest. This occurs when each year, a bank calculates the fixed percentage interest on your account, say 3%, and adds it your total amount. For example, £100 would become £103. Then, at the end of next year, it adds another 3%, but now that 3% amounts to more, because we’re taking 3% of £103 – so it’s like we’re getting interest on last year’s interest, which is precisely what compound interest is. At the end of the two years, your money increases by £3.09 rather than just £3. This works the same for compound decay. Reducing £100 by 3% the first year gives you £97. But then reduce by 3% again and you’re taking 3% of 97, which will be a smaller number. In either case, you may be asked to set up and solve problems surrounding compound growth and decay, and (as always) interpret the answers you get. For example, you should be able to recognise that a question of “how much will £5000 become after 6 years at a 4% compound interest rate become?” amounts to the calculation:

  2. Starter = 84 = 53.76 = 570.96 = 445.2 = 54 Increase 75 by 12% Decrease 64 by 16% Increase 549 by 4% Increase 400 by 5% then by a further 6% Decrease 80 by 10% then by a further 25%

  3. number of years new amount = original amount x (percentage)n multiplier

  4. Compound Interest If you put £500 in a bank for 4 years and were paid 3% interest per year, how much would you have? new amount = original amount x (percentage)n = £500 x 1.034 = £562.75

  5. Compound Interest If you put £100 in a bank for 24 years and were paid 4% interest per year – how much would you have? new amount = original amount x (percentage)n = £100 x 1.0424 = £256.33

  6. Depreciation A car loses 12% of its value each year. What is it worth after 7 years if it cost £12000 when new? new amount = original amount x (percentage)n 12% decrease = 0.88 new amount = £12000 x 0.887 = £4904.11

  7. Answers Compound Interest 1) £562.43 2) £4014.68 3a) £7577.03 3b) £577.03 3c) £7874.05 – more 4) £1739.54 5) 15 years 6) n = 4 Depreciation 1) £142 016.59 2) £279.34 3) £5213.92 4) 6 years 5a) Not simple interest! 5b) 0.8 x 0.8 = 0.64 6) 4 years

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