PERCENTAGES 3
Reverse percentages
Sometimes you are told the final value after a percentage change and you have
to find the original value.
This process is referred to as carrying out a reverse percentage.
Reminder:
If a value is increased by 16% the multiplying factor is 1.16 (1+ 0.16)
If a value is decreased by 16% the multiplying factor is 0.84 (1 − 0.16)
HOUSE FOR SALE
Price reduced by 12%.
Now $227 040.
Example
1 Find the original price of the house.
check: 258 000 x 0.88 = 227 040
Car depreciated by
18% in the first year.
Value after first year
= $16 400
Example
2 Find the original value of the car.
check: 20 000 x 0.82 = 16 400
Plant increases in height by
4% in one day.
It now has a height of
41.6 cm.
Example
3 Find the height of the plant yesterday.
check: 40 x 1.04 = 41.6
Simple interest
With simple interest, the interest earned is not reinvested.
This means that the amount earned each year is unchanged.
Example
Calculate the value of the investment after 3 years.
Amount invested = $250
Simple interest rate = 4%
1
Example
Calculate the value of the investment after 4 years.
Amount invested = $1350
Simple interest rate = 2.5%
2
Compound interest
With compound interest, the interest earned is reinvested.
This means that the amount earned each year increases.
Example
Calculate the value of the investment after 2 years.
Amount invested = $800
Compound interest rate = 5%
1
Quick method:
Example
Calculate the value of the investment after 3 years.
Amount invested = $600
Compound interest rate = 2%
2
Quick method:
Example
Calculate a the value of the investment after 8 years
b the amount of interest earned in the 8 years.
Amount invested = $1200
Compound interest rate = 3.5%
3
a
b