1. Compound Interest
When we save with a bank the bank pays us interest at the end of each year.
If we leave the money alone then the interest gets added to our balance giving us a bigger balance.
The next time we calculate the interest it is a % of a larger sum than before.
Example
Suppose we put £500 into an account which pays a rate of 4% per annum. How much is this worth after 3 years?
How much interest do we get for the 3 years?

2. Long Method
4% = 0.04
Int in year 1 = 0.04 X £500
= £20
Balance after 1st year = £520
Int in year 2 = 0.04 X £520
= £20.80
Balance after 2nd year = £540.80
Int in year 3 = 0.04 X £540.80
= £21.632
= £21.63
Balance after 3rd year = £562.43
Interest gained in 3 years = £ £500
= £62.43

3. Quick Method
Adding 4% gives us
104% or so
Balance after year 1 = 1.04 X £500
= £520
Balance after year 2 = 1.04 X £520
= £540.80
Balance after year 3 = 1.04 X £540.80
= £
= £
Again total interest = £62.43

4. Really Quick Method
Adding 4% gives us
104% or
We multiply by 1.04 on three occasions so
Balance after year 3 = 1.04 X 1.04 X 1.04 X £500
= (1.04)3 X £500
= £
= £
Use the xy button
Again total interest = £62.43

5. APPRECIATION - Growing in value.
Example
When it is growing a baby shark’s weight increases by 18% per week. If a baby shark is currently 40kg then how heavy will it be in 5 weeks time ? (to the nearest kg)
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18% more gives us
118% or 1.18
Weight in 5 weeks =
1.18 X 1.18 X 1.18 X 1.18 X 1.18 X 40kg
= 91.51…kg
= 92kg

6. DEPRECIATION - Loss of value.
Example
For each km you climb a mountain the amount of oxygen in the air becomes 13% less.
The air at ground level contains 20 units of oxygen. How many units will there be at the top of Mount Everest which is 8km high?
******************
13% less gives us
87% or
Oxygen level =
0.87 X 0.87 X 0.87 X 0.87 X 0.87 X 0.87 X 0.87 X 0.87 X 20 units
= units
Hence need for masks!!

7. Example
The Simpsons buy a house for £ The following year it is worth £ What is the rate of appreciation?
************
Actual increase =
£ £80000 = £4000
% increase = 400080000
= 0.05
or 5%

8. Example
On its first bounce a pogo stick reaches a height of 48cm.
On its second bounce it only reaches a height of 42cm.
What is the % depreciation in height?
*************
Actual change =
48 – 42 = 6
% change = 6  48
= 0.125
or 12.5%

9. Example
A car completes one lap of a track at 87mph.
It then completes a second lap at 78mph.
Find the % drop in speed!
*************
Actual drop =
= 9 mph
% drop =
9  87
= …..
= 0.103
= 10.3%

10. Example
The population of town is
This is expected to rise by 8% per annum over the next five years.
***********
8% more = 108% or 1.08
Pop in 5 years =
36000 X 1.08 X 1.08 X 1.08 X 1.08 X 1.08 OR
= X (1.08)5 =
= 52900
To nearest 100.