Repeated Percentage

1
Repeated Percentage Proportional Change
2
Reminder

• How to calculate a PERCENTAGE change

• Decrease 1760 by 15

Left with 85 of 1760
MULTIPLIER of 085
85 of 1760
1760 x 085
1496
3
So.

• We can use this procedure for repeated changes
  such as
• (i) Interest of money in bank account
• (ii) Depreciation of a motor car

4
e.g. Interest on Bank Account
4 000 earns 5 interest each year. How much is
it worth after 3 years?
End of Year 1
4 000 x 105
4 200
COMPOUND INTEREST
4 000 x 1051
4 000 x 105
End of Year 2
4 200 x 105
4 410
4 000 x 1052
4 000 x 105 x 105
End of Year 3
4 410 x 105
4 63050
4 000 x 1053
4 000 x 105 x 105 x 105
5
Simple Interest?

• If an account only receives SIMPLE INTEREST, the
  200 earned in the first year would be the same
  for every year
• In our example, that means

4 000 3 x 200 4 600
6
e.g. Value of a car
David buys a new Ford for 14 000. It loses
value at the rate of 15 each year. How much is
it worth after 3 years?
End of Year 1
14 000 x 085
11 900
14 000 x 0851
14 000 x 085
11 900 x 085
10 115
End of Year 2
14 000 x 0852
14 000 x 085 x 085
End of Year 3
10 115 x 085
8 59775
14 000 x 0853
14 000 x 085 x 085 x 085
7
Proportionate Increase

• Andrew said he would increase his donation to
  charity by 6 each year. He starts with 120. How
  much did he give after 5 years?
• After 1 year 120 x (106)
• 12720
• After 5 years 120 x (106)5
• 16059 to nearest penny