Contents

1. 1 Percentages Contents 1.1 Percentages 1.2 Percentage Change 1.3 Profit and Loss 1.4 Discount 1.5 Interest 1.6 Growth and Depreciation 1.7 Successive and Component Percentage Change 1.8 Rates and Taxation in Hong Kong

2. For example, (b) 1.1 Percentages A percentage is a fraction in which the denominator is equal to 100. Example 1 Change each of the following into percentage. (a) 0.83 Solution :

3. 1.2 Percentage Change New value =X(1 + r %) New value =X(1 – r %) • When a value X is increased by r%, we can calculate the new value as follows. • When a value X is decreased by r%, we can calculate the new value as follows. • When an original value is changed to a new value, the percentage change of the value can be measured in the following way.

4. If the answer is positive, it means a percentage increase. If the answer is negative, it means a percentage decrease. 1.2 Percentage Change Example 2 Peter’sweight decreases from 60 kg to 48 kg. Find the percentage change of his weight. Solution :  Percentage decrease of weight is 20%.

5. 1.3 Profit and Loss The profit and loss in trading refers to the difference between the cost price and the selling price. The selling price can be found if the cost price and the percentage change are given.

6. 1.3 Profit and Loss When the percentage change is positive, it means there is a profit. When the percentage change is negative, it means there is a loss. Example 4 David bought a car for $90 000 three years ago. He sells the car for $54 000 this year. What is the percentage change of his car’sprice? Solution :  Loss percentage of car’s price is 40%.

7. 1.4 Discount Discount is a price deduction from a marked price in purchasing. Example 5 The marked price of a washing machine is $4500. If the selling price is $3000, find the discount percentage. Solution :

8. 1.5 Interest Compound interest can only be found by A – P. Let P be the principal, I be the interest, A be the amount, r% be the interest rate per period and n be the number of periods. (a) Simple Interest (b) Compound Interest

9. 1.5 Interest p.a. means ‘per annum’, that is, per year. Since it is compounded half-yearly, the number of periods in two years is 2  2 = 4. The interest per period is Example 6 If $15 000 is invested at 10% p.a. for two years, compounded half-yearly, find the total amount that can be received after two years. (Give the answer correct to the nearest dollar.) Solution : (correct to the nearest dollar)

10. New value =P(1 + r %)n New value =P(1 – r %)n 1.6 Growth and Depreciation (a) Growth If an original value P grows with a rate of r% in a period of time, then the new value after n periods is given by: (b) Depreciation If an original value P depreciates with a rate of r% in a period of time, then the new value after n periods is given by: Notes: (1 + r %)is called the growth factor and (1 – r %)n is called the decay factor.

11. 1.6 Growth and Depreciation Example 7 The population of a town is growing at a rate of 8% each year. If the population is 50 000 at this moment, what is the population after three years? (Give the answer correct to the nearest hundred.) Solution : (correct to the nearest dollar)

12. 1.7 Successive and Component Percentage Change A. Successive Percentage Change Example 8 The total amount of unemployed in Hong Kong was 207 500 in 1999. The unemployment rate was decreased by 19.6% from 1999 to 2000, but was increased by 4.7% from 2000 to 2001 and continuously increased by 46.2% from 2001 to 2002. What is the total amount of unemployed in 2002? (Give the answer correct to the nearest integer.) Solution : (correct to the nearest integer)

13. 1.7 Successive and Component Percentage Change B. Component Percentage Change Example 9 The total cost of making a car is divided into two parts, which are $50 000 in human resources and $30 000 in materials. If the cost of human resources and materials are increased by 20% and 50% respectively, what is the percentage change of the total cost? Solution :

14. 1.8 Rates and Taxation in Hong Kong For the Hong Kong financial year 2003-2004, the rates percentage charge is 5%. Rates are usually paid quarterly. A. Rates Rates are charged at a percentage of the rateable value which is the estimated annual rental value of a property, with an assumption that the property is vacant and to be let. Example 10 The rateable value of a flat is $350 000. Find the rates quarterly if the rates are charged at 5% per year. Solution :

15. 1.8 Rates and Taxation in Hong Kong For the Hong Kong financial year 2003-2004, the tax rates set on different net chargeable income are: 2% on the first $30 000; 8% on the next $30 000; 14% on the next %30 000 and 20% on the remaining. Net chargeable income = Annual income - Deductions Salaries tax = Net chargeable income  Tax rate B. Taxation (a) Salaries Tax Salaries tax is charged on the annual income received from an employment. Step 1 : Calculate the net chargeable income. Step 2 : Calculate the salaries tax.

16. 1.8 Rates and Taxation in Hong Kong Example 11 Calculate the salaries tax in the year of 2004-2005 if the net chargeable income is $150 000. Solution : First divide the net chargeable income into four parts:

17. For the Hong Kong financial year 2003-2004, the property tax rate is 16%. Net assessable value = Annual rent – Allowances Property tax = Net assessable value Tax rate 1.8 Rates and Taxation in Hong Kong (b) Profits Tax and Property Tax Profits tax is charged on the net profits made from business. Property tax is charged on the owner of a piece of land or a building who receives rent from the property. Step 1 : Calculate the net assessable value. . Step 2 : Calculate the property tax .

18. 1.8 Rates and Taxation in Hong Kong Net assessable value = Annual rent – Rates in a year – Allowances Property tax = Net assessable value Tax rate If the owner is responsible for the payment of the rates of property, the property tax is calculated as follows: Step 1 : Calculate the allowances. Step 2 : Calculate the net assessable value. Step 3 : Calculate the property tax.

19. 1.8 Rates and Taxation in Hong Kong Example 12 Miss Yuen owns a flat, which have a rateable value of $800 000, in Shatin. She lets the flat out to Mr. Wong at a monthly rent of $8000. (a) Find the property tax paid by Miss Yuen if she does not need to pay the rates. Solution :

20. 1.8 Rates and Taxation in Hong Kong Example 12 Miss Yuen owns a flat, which have a rateable value of $800 000, in Shatin. She lets the flat out to Mr. Wong at a monthly rent of $8000. (b) Find the property tax paid by Miss Yuen if she also needs to pay the rates. Solution :