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Compound Interest: Methods and Formulas

Learn about compound interest calculations, formulas, and examples for exponential growth and decay. Explore how investments grow over time using different methods and understand the general shape of exponential growth and decay graphs.

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Compound Interest: Methods and Formulas

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  1. Compound Interest Amount invested = £1000 Interest Rate = 5% Method 1 Interest at end of Year 1 = 5% of £1000 = £50 = 0.05 x£1000 Amount at end of Year 1 = £1050 Interest at end of Year 2 = 5% of £1050 = £52.50 = 0.05 x£1050 Amount at end of Year 2 = £1050 + £52.50 = £1102.50 and so on

  2. Compound Interest Amount invested = £1000 Interest Rate = 5% Method 2 Amount at end of Year 1 = 105% of £1000 = 1.05 x£1000 = £1050 = £1102.50 Amount at end of Year 2 = 1.05 x£1050 and so on

  3. Example – Compound Interest £1000 invested at 5% interest 1050.00 1102.50 1157.63 1215.51 1276.28

  4. Compound Interest Amount invested = £1000 Interest Rate = 5% Method 3 = 1.05nx£1000 Amount at end of Year n = 1.052x£1000 = £1102.50 Amount at end of Year2 = 1.0510x£1000 = £1628.89 Amount at end of Year10

  5. General Formulae Exponential Growth y = kamx k, a and m positive a > 1 Example – Compound Interest A = 1.05nx£1000 x is n y is A a = 1.05 k = 1000 m = 1 Can be written in other forms: A = 1.10250.5nx£1000 k = 1000 a = 1.1025 m = 0.5

  6. Example – Radioactive Decay Plutonium has a half-life of 24 thousand years 500 24 250 48 125 72 62.5 96 120 31.25

  7. A = 1000 x2-0.0416t where t = time in thousands of years Example – Radioactive Decay of Plutonium Decay functions A = 1000 x0.5n where n = no. of half lives A = 1000 x2-n where n = no. of half lives A = 1000 x2-t/24where t = time in thousands of years Exponential Decay a < 1 m positive k and a positive y = kamx a > 1 m negative

  8. General Shape of Graphs Exponential Growth Exponential Decay

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