Definition 1
A percentage is a fraction with a denominator of 100, and the % symbol is used to represent percentages.
To convert a fraction or decimal into a percentage:
Multiply by 100%
To convert a percentage into a fraction:
1. Drop the % sign
2. Divide by 100
3. Reduce to lowest terms
To find the percentage of a number:
1. Rewrite the percentage as a fraction
2. Multiply the number by the fraction
To express one quantity, a, as a percentage of another quantity, b:
1. Write a as a fraction of b
2. Multiply the fraction a/b by 100%
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Definition 2
Discount
A discount is the reduction in price of an item, which equals to marked price - selling price.
E.g. If Marc bought a guitar whereby its price had been reduced by 30% and he paid $294,
Sale price = $294 = 70/100 x marked price
Marked price = $294 x 100/70 = $420
Commision
When an agent buys or sells an item on behalf of another person, he is paid a commision.
Profit/Loss
If an item is sold at a higher price than the cost price, then a profit is made. The reverse is true when the shop incurs a loss.
All these three concepts will make use of percentages in their calculations.
Simple Interest
Refers to interest calculated on the original principal. The formula to calculate simple interest is given below:
I = PRT/ 100
Where I = Simple interest
P = Principal
R = Rate (per annum) and
T = Time (in years)
Compound Interest
Refers to interest that is not calculated based on the original principal sum but compounded annually. The formula to calculate compound interest is given below:
A = P(1 + R/100)n
Where A = Amount
P = Principal
R = Rate of interest and
n = Number of interest periods
Hire Purchase, Money Exchange and Taxation
Hire Purchase
When we buy goods by hire purchase, the payment is made over a specified period through regular instalments. Normally a deposit or an initial down payment is required.
Money Exchange
To convert from one currency to another, find the unit equivalent of the first currency to the second. For example, if the exchange rate of Singapore dollars and Malaysian ringgit is S$1 = RM2.39, and you have to calculate, in Malaysian ringgit, the amount received for S$500, you do:
S$1 = RM2.39
S$500 = 500 x RM2.39 = RM1195
Taxation and GST
1. Goods and Services Tax (GST)
In Singapore, a 7% tax is added to the cost of goods and services by the government. This is called the goods and services tax (GST). In other countries, it is known as the value-added tax (VAT).
2. Property Tax
A property tax is imposed on owners of land, houses, flats or buildings. It is based on the annual value of the property. The annual value is the expected amount of rent if the property is rented out for a year.
3. Income Tax
Income tax is imposed on all income derived during the year from 1 January to 31 December. It is calculated based on the chargeable income.
Chargeable income = Total income - Reliefs
