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S5_Int2_Calculating_Percentages

# S5_Int2_Calculating_Percentages - Calculating Percentages...

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Unformatted text preview: Calculating Percentages Int 2 www.mathsrevision.com Simple Interest / Compound Compound Interest Appreciation / Depreciation Inflation / Working back Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 1 Starter Int 2 Q1. Round t he f ollowing t o 2 decimals places. (b) 4. 55732 (c) 3. 98111 www.mathsrevision.com (a) 3. 5647 Q2. Writ e in st andard f orm. (a) 12300 (b) 0. 0034 (c) 0. 0005 Q3. Writ e out in f ull. (b) 1. 19 x 10 - 2 (c) 4. 5 x 10 - 1 2 (a) 2. 8 x 10 3 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com Calculating Percentages Int 2 Compound Interest Appreciation More Simple Interest www.mathsrevision.com Just Calculating Percentages Working backwards Monday, February 13, 2012 Inflation Rising Prices created by Mr. lafferty @ www.mathsrevision.com Depreciation Less 3 Calculating Percentages Int 2 Learning Intention Success Criteria 1. To know the meaning of the term simple interest. 2. To know the meaning of the term compound interest. 3. Know the difference between simple and compound interest. www.mathsrevision.com 1. To understand the term simple interest and compound interest. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 4 Calculating Percentages Int 2 Just working out percentages Simple Interest www.mathsrevision.com I have 400 in the Bank. At the end of each year I receive 7% of 400 in interest. How much interest do I receive after 3 years. How much do I now have? I nt erest = 7 100 400 = 28 Af t er 3 years int erest is 3 x 28 = 84. Tot al in bank is = 400 + 84 = 484 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 5 Calculating Percentages Int 2 www.mathsrevision.com Now try Exercise 1 Ch2 (page 8) Odd Numbers Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 6 Calculating Percentages Interest calculated Int 2 Compound Interest www.mathsrevision.com on new value every year Real life Interest is not a fixed quantity year after year. One year's interest becomes part of the next year's amount. Each year's interest is calculated on the amount at the start of the year. Principal value Example Daniel has 400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the simply interest and then the compound interest after 3 years. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 7 Calculating Percentages Int 2 Compound Interest Interest calculated on new value every year www.mathsrevision.com Daniel has 400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the compound interest and the amount he has in the bank after 3 years. Simple Interest Interest = 7% of 400 = 28 3 x 28 = 84 Y1 : Interest = 7% of 400 = 28 Amount = 400 + 28 = 428 Y 2 : Interest = 7% of 428 = 29.96 Amount = 428 + 29.96 = 457.96 Y 3 : Interest = 7% of 457.96 = 32.06 Amount = 457.96 + 32.06 = 490.02 Simple Interest is only 84 Monday, February 13, 2012 Compound is 490.02 400 = 90.02 created by Mr. lafferty @ www.mathsrevision.com 8 Calculating Percentages Int 2 www.mathsrevision.com Now try Exercise 2 Ch2 (page 8 & 9) Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 9 Starter Int 2 Q 1. Ro und t h e f o llo wing t o 2 d e c im als plac e s . www.mathsrevision.com (a) 4 .6 6 6 4 7 (b ) 8 .7 5 7 3 2 (c ) 7 .4 9 111 Q 2 . W r it e in s t and ar d f o r m . (a) 3 0 0 (b ) 0 .0 4 (c ) 0 .0 10 5 Q 3 . Find t h e c o m po und int e r e s t o n 2 0 0 o ve r 2 y e ar s at 10 % int e r e s t . Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 10 Calculating Percentages Int 2 Learning Intention Success Criteria 1. To calculate compound interest using calculator.. 2. Show appropriate working when solving problems. www.mathsrevision.com 1. To understand how to use the calculator to calculate compound interest easier. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 11 Calculating Percentages Int 2 Using a calculator to do Compound Formula Using a calculator to do This is called the multiplier. www.mathsrevision.com % V = I1 100 n n = period of time Days, months years I = initial value = increase or decrease V = Value 12 IMPORTANT Can only use this when percentage is fixed Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com Calculating Percentages Int 2 Using a calculator to do Compound questions Using a calculator www.mathsrevision.com Calculate the money in the bank after 3 years if the compound interest rate is 7% and the initial value is 400. n = 3 I =400 = increase 1+0.07=1.07 % V = I1 100 3 n V= 400 x (1.07) = 490.02 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 13 Calculating Percentages Int 2 Using calculator to calculate Compound questions Using calculator www.mathsrevision.com In a jar bacteria grows 4% every hour. Initially there were 200 bacteria in the jar. How many bacteria are in the jar 4 hours later. % V = I1 100 4 n n = 4 I =200 = increase 1+0.04=1.04 Monday, February 13, 2012 V= 200 x (1.04) = 234 created by Mr. lafferty @ www.mathsrevision.com 14 Calculating Percentages Int 2 Using calculator to calculate Compound questions Using calculator www.mathsrevision.com A car reduces in price by 14% each year. Initially it cost 12 500. much is it worth 5 years later. % V = I1 100 5 n n = 5 I =12 500 = increase 10.14=0.86 Monday, February 13, 2012 V= 12 500 x (0.86) = 5880.34 created by Mr. lafferty @ www.mathsrevision.com 15 Calculating Percentages Int 2 www.mathsrevision.com Now try worksheet Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 16 Starter Int 2 Q 1. W r it e o ut in f ull. www.mathsrevision.com (a) 8 .5 6 7 10 3 (b ) 2 .6 10 1 Q 2 . W r it e in s t and ar d f o r m . (a) 10 0 (b ) 0 .0 3 5 Q 3 . Find t h e c o m po und int e r e s t o n 6 0 0 o ve r 2 y e ar s at 5 % int e r e s t . Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 17 Calculating Percentages Int 2 Learning Intention Success Criteria 1. To know the terms appreciation and depreciation. 2. Show appropriate working when solving problems containing appreciation and depreciation. www.mathsrevision.com 1. To understand the terms appreciation and depreciation. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 18 Calculating Percentages Int 2 www.mathsrevision.com Appreciation / Depreciation Appreciation : Going up in value e.g. House value Depreciation : Going down in value e.g. car value Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 19 Quicker Method Easier Average house price in Ayr has appreciated by 79% over past 10 years. If you bought the house for 64995 in 1994 how much would the house be worth now ? 1.79 x 64995 = 116341.05 Appreciation = 79% x 64995 = 0.79 x 64995 = 51346.05 New value = Old Value + Appreciation = 64995 + 51346.05 = 116341.05 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com Just working out percentages 20 Calculating Percentages Int 2 A Mini Cooper cost 14 625 in 2002 At the end 2003 it depreciated by 23% At the end 2004 it will depreciate by a further 16% What will the mini cooper worth at end 2004? End 2003 Depreciation = 23% x 14625 = 0.23 x 14625 = 3363.75 New value = Old value Depreciation = 14625 3363.75 = 11261.25 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com www.mathsrevision.com 21 Calculating Percentages Int 2 End 2003 Depreciation www.mathsrevision.com New value End 2004 Depreciation = 23% x 14625 = 0.23 x 14625 = 3363.75 = Old value Depreciation = 14625 3363.75 = 11261.25 = 16% x 11261.25 = 0.16 x 11261.25 = 1801.80 = 11261.25 1801.80 = 9459.45 New Value Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 22 Calculating Percentages Int 2 www.mathsrevision.com Now try MIA Ex 4 Ch2 (page 12) Odd Numbers Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 23 Starter Int 2 Q 1. W r it e t h e s e pe r e c e nt ag e s as d e c im a ls . www.mathsrevision.com (a) 5 0 % (b ) 2 5 % (c ) 6 0 % Q 2 . Find 4 0 % o f 4 0 0 . Q 3 . Find t h e ar e a o f t h e s h ape . 5cm Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 6cm 24 Calculating Percentages Int 2 Learning Intention Success Criteria 1. Know the term inflation. 2. Work out reallife problems involving inflation. www.mathsrevision.com 1. Understand term inflation and work out associated reallife problems. Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 25 Calculating Percentages Measure of how Int 2 www.mathsrevision.com Example 1 Inflation is normally given in percentage form and is normally in the range 0 10% In 2004 a worker received a wage of 300 per week. If inflation is 2% in 2004, what should be his wage be in 2005. Inflation much prices rise each year. 2004 inflation = 2% 2% of 300 = 6 His wage should be 300 + 6 = 306 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 26 Calculating Percentages Int 2 www.mathsrevision.com Example 2 Inflation is normally given in percentage form and is normally in the range 0 10% In 2002 a CD cost 8. The cost increases in line with inflation. What is the price in 2003 if inflation is 1.5%. Inflation Measure of how much prices rise each year. 2002 inflation = 1.5% 1.5% of 8 = 0.12 Price is 8 + 0.12 = 8.12 Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 27 Calculating Percentages Int 2 www.mathsrevision.com Now try MIA Ex 6 Ch2 (page 15) Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 28 Calculating Percentages Int 2 Example 1 Reversing the change After a 10% increase the price of a house is 88 000. What was the price before the increase. www.mathsrevision.com Deduce from question : We have : 100 % + 10 % = 88 000 110 % = 88 000 1 % : 88 000 Price before is 100% : Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 110 = 800 29 800 x 100 = 80 000 Calculating Percentages Int 2 Example 2 Reversing the change www.mathsrevision.com The value of a car depreciated by 15%. It is now valued at 2550. What was it's original price. Deduce from question : We have : 1 % : Price before is 100% : Monday, February 13, 2012 100 % - 15 % = 2 550 85 % = 2 550 2 550 85 = 30 30 x 100 = 3 000 30 created by Mr. lafferty @ www.mathsrevision.com Calculating Percentages Int 2 www.mathsrevision.com Now try MIA Ex 7 Ch2 (page 17) Monday, February 13, 2012 created by Mr. lafferty @ www.mathsrevision.com 31 ...
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