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

2. 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
£ £100 = £2100
£2100 x 5% = £105
£ £105 =£2205
£2100
£2205 x 5% = £110.25
£ £ =£
£2205

3. 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 £
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!!

4. 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 % !!)

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 periods
Using the formula I =
= ?
= £900
So interest is £900 and the account has £3900

6. 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.

7. 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 £
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 £

8. 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 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

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!

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