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© T Madas

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£10000 are invested in a building society account. The account pays an annual interest of 8%. Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn. This problem would be easy if banks/building societies paid SIMPLE INTEREST: I.e. 8% on the original amount for every year Then: 8% of £10000 6 x £800 £10000 + £4800 Is this what usually happens? = £800 = £4800 = £14800

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© T Madas End of YearInterest CalculationStart of YearYear 1080010000 x 1.08100001 1166410800 x 1.08108002 15868.7414693.28 x 1.0814693.286 13604.89 x 1.0813604.895 12597.12 x 1.0812597.124 11664 x 1.08116643 This is what usually happens

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© T Madas This is known as the compound interest calculation, when at the end of a given period, say a year, the “capital” and interest is reinvested in a repetitive fashion for a number of years.

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Can you spot an easier calculation? £10000 are invested in a building society account. The account pays an annual interest of 8%. Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn.

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© T Madas Can you spot an easier calculation? Original amount Interest increase as a % multiplier years £10000 are invested in a building society account. The account pays an annual interest of 8%. Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn. 10000x 1.08 ( ) ( ) ( ) ( ) ( ) = 10000x 1.08 = 10000x (1.08) 6

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© T Madas Can you spot an easier calculation? £10000 are invested in a building society account. The account pays an annual interest of 8%. Calculate the amount in this account in 6 years time, if no money is further paid in or withdrawn. 10000x 1.08 ( ) ( ) ( ) ( ) ( ) = 10000x 1.08 = remember the order of operations 10000 x1.586874 15868.74 = = 10000x (1.08) 6

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© T Madas

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( ) 7 £1000 were invested at a compound interest rate of 5% per annum. Calculate the value of this investment in 7 years, 15 years and 25 years time. In 7 years: 1000x 1.05= 1407.10 ( ) 15 In 15 years: 1000x 1.05= 2078.93 ( ) 25 In 25 years: 1000x 1.05= 3386.35

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© T Madas

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How much more does £1000 invested at 10% compound interest for 10 years gain than £1000 invested at 10% simple interest? Simple interest: 10% of 1000 is £100 10 years earning £100 per year gains £1000 The investment doubles to £2000 Compound interest: ( ) 10 1000 x 1.1 = 2593.74 an extra £593.74

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© T Madas

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How many years will it take £100 to double in value when invested at: 1. 5% simple interest 2. 5% compound interest Simple interest: 5% of 100 is £5 Every year £5 is earned For the investment to double another £100 must be gained 100 ÷ 5 = 20 years

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© T Madas Compound interest: In order for the £100 to double the investment must be worth £200 in n number of years ( ) n 100 x 1.05 = 200 This is an equation which requires logarithms to solve We are going to use trial and improvement How many years will it take £100 to double in value when invested at: 1. 5% simple interest 2. 5% compound interest

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© T Madas ( ) 10 100x 1.05= 162.89 n = 10 ( ) 15 100x 1.05= 207.89 n = 15 ( ) 14 100x 1.05= 197.99 n = 14 Is the correct answer 14 or 15 years? In order for the £100 to double the investment must be worth £200 in n number of years ( ) n 100 x 1.05 = 200 How many years will it take £100 to double in value when invested at: 1. 5% simple interest 2. 5% compound interest Compound interest:

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