### Percentage

Transcript: Chapter 3 Percentage Percentage Changes Percentage Change Step 1 Find the Original/New Value Step 3 Give answer statement Percentage change = New Value - Original Value Original Value x100% Step 2 Apply the Formula The base radius and the height of a cylinder are 4 cm and 8 cm respectively. If the base radius increases by 25% and the height decreases by 40%, find (a) the new volume of the cylinder, (b) the percentage change in the volume of the cylinder. Find the original/new value Answer Answer Mr Wu has investments which worth $2300 000. It consists of 10% shares, 20% cash and 70% property. After 1 year, the value of his shares and the amount of cash have increased by 8% and 2% respectively, while the value of his property has fallen by 15%. Find (a) the new value of Mr Wu’s total investments, (b) the percentage change in the value of Mr Wu’s total investments. Further Example Answer Answer [2015_A1_Q6] The cost of a book is $250. The book is now sold and the percentage profit is 20%. (a) Find the selling price of the book. (b) If the book is sold at a discount of 25% on its marked price, find the marked price of the book. Marked price/Selling Price & Profit/Loss Percentage Profit/Loss % Answer Answer % Change involves ratio % change involves ratio Last year, 35% of the members in a fitness centre were females. The numbers of female members and male members in the fitness centre this year are decreased by 20% and 10% respectively. Find the percentage change in the number of members in the fitness centre. Answer Answer The volume of water in a lake is 6000 m^3 in a certain year. In the coming 3 consecutive years, the volume of water in the lake decreases at a rate of 5% per year. Then, the volume of water in the lake increases by 8% in the following year. Find the overall percentage change in the volume of water in the lake after 4 years. Increase/Decrease at a constant rate Z = Y(1+20%) Y= X (1+10%) Z = Y(1+20%)= X (1+10%)(1+20%) Answer Answer The value of an equipment in a factory depreciated from $750 000 in Dec 2015 to $541 875 in Dec 2016 at a constant rate of x% every 6 months. (a) Find the value of x. (b) If the depreciation rate per 6 months was constant from Jun 2014 to Dec 2016, find the value of the equipment in Jun 2014. (Give your answer correct to the nearest integer.) Further Example Answer Answer Interest Simple Interest Compound Interest Example Simple Interest Example Carol deposits $12 000 in Bank A at a simple interest rate of 3.5% p.a. and $15000 in Bank B at a simple interest rate of 2% p.a.. Find the total simple interest she will receive after 2 years. Answer Answer Emily borrows $30 000 from a bank for 3 years. If the annual interest rate is tripled, she will need to repay an additional simple interest of $6300. What is the original annual interest rate? Further Example Further Example Answer Answer Compound Interest Compound Interest Example Andrew deposits $8000 in a bank at an interest rate of 4% p.a. Find the compound interest he will obtain 3 years later if the interest is compounded (a) yearly, (b) half-yearly. Answer Answer Mr Chan deposited a sum of money in a bank at an interest rate of 8% p.a. compounded monthly. After 6 years, he obtained an interest of $11 350. Find the principal that Mr Chan deposited. (Give your answer correct to the nearest integer.) Finding Principal Further Example Answer Answer Nick deposits $50 000 in a bank. The interest is compounded half-yearly. After 1 year, he receives a compound interest of $3045. (a) Find the annual interest rate. (b) The amount received after 1 year is then deposited in another bank at the same interest rate, but the interest is compounded monthly. What will be the amount received after another 1 year? (Give your answer correct to the nearest integer.) Finding Rate Further Example Answer Answer Taxation Taxation & Enrichment Rates The rateable value of a property is $900 000. If the rates are charged at 5% p.a., find the rates payable per quarter. Example Answer Answer The rateable value of a flat increases at a constant rate of 4% per year. The owner of the flat paid $6000 per quarter for the rates in 2008. If the rates are charged at 5% p.a., find the rates that the owner should pay in 2016. (Give your answer correct to the nearest integer.) Further Example Further Example Answer Answer Property Tax Example Property Tax A flat is rented out at $6000 per month. If the property tax rate is 15%, find the property tax the owner should pay. Answer Answer Gilbert owns a flat and he wants to get a net monthly income of $16 500 from renting out his flat after paying property tax. If the property tax rate is 15%, find the monthly rent he should charge. Further Example Further Example Answer Answer Example Salary Tax The annual income of Clovis is $350 000 in the financial year 2016/17. If his allowance is $192 000, how much salaries tax should he pay? The table below shows the salaries tax rate for the financial year 2016/17: Net