2This is best worked out using a table: Starting capital Interest £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 capitalInterestNew capitalYr 1£2000Yr 2Yr 3£2000 x 5% =£100£ £100 = £2100£2100 x 5% = £105£ £105 =£2205£2100£2205 x 5% = £110.25£ £ =££2205
3As 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 £If we just use simple interest we would getWhich amounts to £300I =This is £15.25 less than with compound interest.If we work out the interest over a longer period, the extra earnings become incredible!!
4A little more on simple interest The formula we use is:I =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 % !!)
5= ? 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 periodsUsing the formula I == ?= £900So interest is £900 and the account has £3900
6Compound 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.
7From the table: The interest earned is £312.16 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?From the table: The interest earned is £312.16And the account holds £CapitalInterestNew CapitalYr 1£2500Yr 2Yr 3£2600£2500 x 4% = £100£2600£2600 x 4% = £104£2704£2704£2704 x 4% = £108.16£
8Now 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?Rounding the answer (since we cannot have 0.9 of a seal) we have a population of seals!Start PopulationDecreaseNew PopulationYr 112500Yr 2Yr 3Mmmm…. problem we cannot have a decimal fraction for the number of seals!!!12500 x 2% = 250SUBTRACT122501225012250 x 2% = 24512005SUBTRACT1200512005 x 2% = 240.1SUBTRACT
9Compound interestThere is a formula to work out the amount in the bank after a number of years:A = C x 1.RnWhere A = amount in bankC = Capital investedR= interest rate ( eg 5% becomes 1.05)n = number of years investedBut you do not need to remember this formula!
10Compound interestExample £2000 invested for 25 years at 5% compound interest gives:£2000 xIn the bank will be £If the same money was invested at simple interest:I = 2000 x 5% x 25 = £2500In the bank will be £ £2500= £4500