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Published byFinn Audley Modified about 1 year ago

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Compound Interest “Interest earning interest” And Simple Interest

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£2000 is invested for 3 years at 5% compound interest. What is in the account after the three years? This is best worked out using a table: Starting capital InterestNew capital Yr 1£2000 Yr 2 Yr 3 £2000 x 5% =£100 £2000 + £100 = £2100 £2100 £2205 £2100 x 5% = £105 £2100 + £105 =£2205 £2205 x 5% = £110.25 £2205 + £110.25 =£2315.25

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As you can see, each new year the capital is increased by the amount of interest earned. After the three year investment period, the account has £2315.25 If we just use simple interest we would get Which amounts to £300 This is £15.25 less than with compound interest. If we work out the interest over a longer period, the extra earnings become incredible!! I =

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A little more on simple interest The formula we use is: Where “I” is the interest earned over the period “c” is the initial capital invested “r” is the interest rate (ignore the %) And “t” is the period of time invested (The dividing by 100 is because the rate is a % !!) I =

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Another worked example of simple interest: £3000 is invested for 5 years at 3% interest every 6 months. How much interest is earned and how much would the account contain? 5 years = 10 x 6month periods Using the formula I = = £900 So interest is £900 and the account has £3900 = ?

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Compound interest is what is use by Banks, Building Societies, etc. It also relates to the growth of living organisms. The new growth of a tree also grows!! There is also a negative version which relates to a compound DECREASE. The only difference is that we TAKE away the “interest” and the reduced amount becomes the new starting value each time.

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You try this one £2500 is invested for 3 years at 4% compound interest each year. How much interest is earned and how much would be in the account? CapitalInterestNew Capital Yr 1£2500 Yr 2 Yr 3 £2500 x 4% = £100 £2600 £2600 x 4% = £104£2704 £2704 x 4% = £108.16 £2812.16 From the table: The interest earned is £312.16 And the account holds £2812.16

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Now a decrease calculation The seal population off the Norfolk coast is decreasing by 2% each year. Last summer the seal population was 12500, what will it be in 3 summers time? Start Population DecreaseNew Population Yr 1 12500 Yr 2 Yr 3 12500 x 2% = 250SUBTRACT12250 12250 x 2% = 245 SUBTRACT 12005 12005 x 2% = 240.1SUBTRACT 11764.9 Rounding the answer (since we cannot have 0.9 of a seal) we have a population of 11765 seals! Mmmm…. problem we cannot have a decimal fraction for the number of seals!!!

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Compound interest There is a formula to work out the amount in the bank after a number of years: A = C x 1.R n Where A = amount in bank C = Capital invested R= interest rate ( eg 5% becomes 1.05) n = number of years invested But you do not need to remember this formula!

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Compound interest Example £2000 invested for 25 years at 5% compound interest gives: £2000 x 1.05 25 In the bank will be £6772.71 If the same money was invested at simple interest: I = 2000 x 5% x 25 = £2500 In the bank will be £2000 + £2500 = £4500

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