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Calculating Percentages. Int 2. Simple Interest / Compound. Compound Interest. www.mathsrevision.com. Appreciation / Depreciation. Inflation / Working back. Int 2. Starter. www.mathsrevision.com. Calculating Percentages. Int 2. Compound Interest. Appreciation More. Simple Interest.

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slide1

Calculating Percentages

Int 2

Simple Interest / Compound

Compound Interest

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Appreciation / Depreciation

Inflation / Working back

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starter

Int 2

Starter

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slide3

Calculating Percentages

Int 2

Compound Interest

Appreciation

More

Simple Interest

Just Calculating Percentages

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Inflation

Rising Prices

Depreciation

Less

Working

backwards

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slide4

Calculating Percentages

Int 2

Learning Intention

Success Criteria

  • To know the meaning of the term simple interest.
  • To understand the
  • term simple interest and compound interest.
  • To know the meaning of the term compound interest.

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3. Know the difference between simple and compound interest.

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slide5

Calculating Percentages

Just working out percentages

Int 2

Simple Interest

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?

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slide6

Calculating Percentages

Int 2

Now try Exercise 1

Ch2 (page 8)

Odd Numbers

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slide7

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.

Calculating Percentages

Interest calculated on new value every year

Int 2

Compound Interest

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.

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Principal value

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slide8

Calculating Percentages

Interest calculated on new value every year

Compound Interest

Int 2

Daniel has £400 in the bank. He leaves it in the bank for 3 years. The interest is 7% each year. Calculate the compoundinterest and the amount he has in the bank after 3 years.

Simple Interest

Y1 : Interest = 7% of £400 = £28

Amount = £400 + £28 = £428

Interest = 7% of £400 = £28

Y 2 : Interest = 7% of £428 = £29.96

3 x 28 = £84

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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

Compound is £490.02 - £400 = £90.02

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slide9

Calculating Percentages

Int 2

Now try Exercise 2

Ch2 (page 8 & 9)

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starter10

Int 2

Starter

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slide11

Calculating Percentages

Int 2

Learning Intention

Success Criteria

  • To calculate compound interest using calculator..
  • To understand how to use the calculator to calculate compound interest easier.
  • Show appropriate working
  • when solving problems.

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slide12

Calculating Percentages

Int 2

This is called the multiplier.

Using a calculator to do Compound Formula

n = period of time

Days, months years

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I = initial value

IMPORTANT

Can only use this when percentage is fixed

± = increase or decrease

V = Value

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slide13

Calculating Percentages

Int 2

Using a calculator to do Compound questions

Calculate the money in the bank after 3 years if the compound interest rate is 7% and the initial value is £400.

n = 3

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I =400

± = increase 1+0.07=1.07

V= 400 x (1.07)3= £490.02

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slide14

Calculating Percentages

Int 2

Using calculator to calculate Compound questions

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.

n = 4

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I =200

± = increase 1+0.04=1.04

V= 200 x (1.04)4= 234

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slide15

Calculating Percentages

Int 2

Using calculator to calculate Compound questions

A car reduces in price by 14% each year. Initially it cost £12 500.

much is it worth 5 years later.

n = 5

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I =12 500

± = increase 1-0.14=0.86

V= 12 500 x (0.86)5= £5880.34

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slide16

Calculating Percentages

Int 2

Now try

worksheet

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starter17

Int 2

Starter

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slide18

Calculating Percentages

Int 2

Learning Intention

Success Criteria

  • To know the terms appreciation and depreciation.
  • To understand the terms appreciation and depreciation.
  • Show appropriate working
  • when solving problems containing appreciation and depreciation.

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slide19

Calculating Percentages

Int 2

Appreciation / Depreciation

Appreciation : Going up in value e.g. House value

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Depreciation : Going down in value e.g. car value

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slide20

Quicker Method

Easier

1.79 x 64995

= £116341.05

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 ?

Appreciation = 79% x £ 64995

  • = 0.79 x £64995

= £ 51346.05

New value = Old Value + Appreciation

= £64995 + £51346.05

= £ 116341.05

Just working out percentages

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slide21

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

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slide22

Calculating Percentages

Int 2

End 2003

Depreciation = 23% x £14625

= 0.23 x £14625

= £3363.75

New value = Old value - Depreciation

= £14625 - £3363.75

= £11261.25

End 2004

Depreciation = 16% x £11261.25

= 0.16 x £11261.25

= £1801.80

New Value = £11261.25 - £1801.80

= £9459.45

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slide23

Calculating Percentages

Int 2

Now try MIA Ex 4

Ch2 (page 12)

Odd Numbers

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starter24

Int 2

Starter

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5cm

6cm

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slide25

Calculating Percentages

Int 2

Learning Intention

Success Criteria

  • Know the term inflation.
  • Understand term inflation
  • and work out associated real-life problems.
  • Work out real-life problems involving inflation.

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slide26

Calculating Percentages

Measure of how much prices rise each year.

Int 2

Inflation

Inflation is normally given in percentage form

and is normally in the range 0 – 10%

Example 1

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.

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2004 inflation = 2%

2% of £300 = £6

His wage should be £300 + £6 = £306

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slide27

Calculating Percentages

Measure of how much prices rise each year.

Int 2

Inflation

Inflation is normally given in percentage form

and is normally in the range 0 – 10%

Example 2

In 2002 a CD cost £8. The cost increases in line with inflation.

What is the price in 2003 if inflation is 1.5%.

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2002 inflation = 1.5%

1.5% of £8 = £0.12

Price is £8 + £0.12 = £8.12

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slide28

Calculating Percentages

Int 2

Now try MIA Ex 6

Ch2 (page 15)

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slide29

Deduce from question :

100 % + 10 % = £88 000

We have :

110 % = £88 000

1 % :

Price before is 100% :

£800 x 100 = £80 000

Calculating Percentages

Int 2

Reversing the change

Example 1

After a 10% increase the price of a house is £88 000.

What was the price before the increase.

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slide30

Deduce from question :

100 % - 15 % = £2 550

We have :

85 % = £2 550

1 % :

Price before is 100% :

£30 x 100 = £3 000

Calculating Percentages

Int 2

Reversing the change

Example 2

The value of a car depreciated by 15%. It is now valued

at £2550. What was it’s original price.

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slide31

Calculating Percentages

Int 2

Now try MIA Ex 7

Ch2 (page 17)

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