“Interest earning interest” Compound Interest “Interest earning interest” And Simple Interest

This 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 capital Interest New capital Yr 1 £2000 Yr 2 Yr 3 £2000 x 5% =£100 £2000 + £100 = £2100 £2100 x 5% = £105 £2100 + £105 =£2205 £2100 £2205 x 5% = £110.25 £2205 + £110.25 =£2315.25 £2205

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 I = This is £15.25 less than with compound interest. If we work out the interest over a longer period, the extra earnings become incredible!!

A 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 % !!)

= ? 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

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.

From 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 £312.16 And the account holds £2812.16 Capital Interest New Capital Yr 1 £2500 Yr 2 Yr 3 £2600 £2500 x 4% = £100 £2600 £2600 x 4% = £104 £2704 £2704 £2704 x 4% = £108.16 £2812.16

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? Rounding the answer (since we cannot have 0.9 of a seal) we have a population of 11765 seals! Start Population Decrease New Population Yr 1 12500 Yr 2 Yr 3 Mmmm…. problem we cannot have a decimal fraction for the number of seals!!! 12500 x 2% = 250 SUBTRACT 12250 12250 12250 x 2% = 245 12005 SUBTRACT 12005 12005 x 2% = 240.1 SUBTRACT 11764.9

Compound interest There is a formula to work out the amount in the bank after a number of years: A = C x 1.Rn 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!

Compound interest Example £2000 invested for 25 years at 5% compound interest gives: £2000 x 1.0525 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