INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Unit 1 Percentages Without a calculator

You should know what these percentages

are as simple fractions.

50% = ½

25% =¼

75% = 3/4

331/3% = 1/3

66 2/3 % = 2/3

10% = 101

It is easier to work out any of these percentages as fractions.

Ex 1. Find 50% of €36.50

Ex 2. Find 25% of €6.40

1

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Ex 3. Find 75% of €36

We can also use 10% = 1 10 to work out other percentages. Find 10% then

times by 2

30%

Find 10% then

times by 3

40%

Find 10% then

times by 4

Find 10% then

times by 7

20%

70%

Ex 4. Find 30% of €3200

Do Exercise 1 Q 1 a to k 2

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Percentages........ with a calculator 17

17% means =

100 28

28% means =

100

14 2 % means = 14.5 1

100

7 % means =

7

100

=

0.17 ...............as a decimal

=

0.28 ...............as a decimal

=

0.145 ...............as a decimal

=

0.07 ...............as a decimal

Ex 1. Find 34% of €76 34% = 0.34

1

Ex 2. Find 16 2 % of €800 16 12 % = 0.165

Ex 3. At a Ceilidh 62.5% of the people attending were female. How many males were there? There were 200 people at the Ceilidh.

Do Exercise 1 Q 1 l to r and Q 3 to 9 3

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Money Simple Interest

You put money in a bank. You leave it there for a period of time.

extra money called Interest. They find a The bank gives you

percentage of what you have in the bank and add it into your account.

The Interest

Rate is given as a

Percentage per annum ( per YEAR )

p.a.

eg. 5% p.a.

7% p.a.

3.4% p.a.

This is the amount of extra money the bank puts in your account if you left your money in the bank for a full year. With Simple Interest the interest added for

2 years would be 3 years would be 4 years would be 6 months would be 3 months would be 5 months would be 7 months would be

1 year interest x 2 1 year interest x 3 1 year interest x 4

1 year interest x 1

2 1 year interest x 1 4 1 year interest x 5 12 1 year interest x 7 12

4

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Ex. 1 John invests £300 in a bank where the interest rate is 5% p.a. What interest does he earn in (a) 1 year (b) 3 years

Ex.2 Amy puts £300 in a bank with a rate of 3.5% p.a.

Calculate the interest earned in (a) 1 year

(b) 4 years

(c) 3 months

(d) 7 months

Find the Percentage................ le

e

mp xa

When buying a £650 cooker. I am asked for a deposit of £97.50. What percentage deposit is this?

Exercise 1

Page 5

Q 10 to 14 5

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Compound Interest Banks don't normally calculate simple interest. They calculate

compound interest. They add your interest into your account at the end of each year. The next year's interest is then worked out on a higher amount.

Example Terry deposits £400 in the bank and leaves it there for 3 years. Rate of Interest = 7% (a) Calculate the amount he will have in his account after 3 years.

(b) Calculate the compound Interest.

Starting Balance =

£400

Year 1 Interest = 7% of £400 = Balance = £400 + £28 =

£28 £428

Year 2 Interest = 7% of £428 =

£29.96

Balance = £428 + £29.96 = £457.96 Year 3 Interest = 7% of £457.96 =

£32.06

Balance = £457.96 + £32.06 = £490.02

(a) Balance after 3 years = £490.02 (b) Compound Interest after 3 years = £490.02 - £400 = £90.02

6

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Example 2 Mrs. Seaton deposits £430 in a bank and leaves it there for three years to gain compound interest at 5% per annum. Calculate how much is in her account after 2 years.

Exercise 2

Page 5

Q 1,3,5

7

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

A quicker method Terry deposits £400 in the bank and leaves it there for 3 years. Rate of Interest = 7% (a) Calculate the amount he will have in his account after 3 years. (b) Calculate the compound Interest.

If 100% is increased by 7%, it goes up to 107% So instead of working out 7% and adding it on. We can find 107% of the balance by using the multipier 1.07

(a)

£400 x 1.073 = £490.02

(b) Compound Interest after 3 years = £490.02 - £400 = £90.02

Interest Rate

Multiplier

5%

105%

1.05

3%

103%

1.03

12%

112%

1.12

3.4%

103.4% 103.4%

1.034 1.034

6 %

106.5%

1.065

1

2

Ex.

%

£600 is invested for 4 years at 7.4%. Find the Compound Interest after 4 years.

£600 x 1.0744

=

Compound Interest =

Exercise 1 Page 5 Q 2 , 7 + do Q 1 again quick way 8

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Appreciation and Depreciation.

Appreciation is the term used when something increases in value over a period of time.

Depreciation

is the term used when something

decreases in value.

Appreciation and Depreciation are usually expressed in percentage terms. Houses tend to appreciate in value over a period of time whereas cars depreciate in value. The starting

percentage at the

beginning of a calculation is

100%.

Appreciation calculations can then be done in a similar way to compound interest calculations but usually on a year to year basis as the rate doesn't always stay fixed.

Appreciation Rate

%

Multiplier

5%

(+100%)

105%

1.05

3%

(+100%)

103%

1.03

12%

(+100%)

112%

1.12

3.4%

(+100%)

103.4%

1.034

6 %

(+100%)

106.5%

1.065

1

2

Ex. 1 Tom bought a house for £125000 last year. Its value has appreciated by 4.5% this year. What is it worth now?

Percent up to

100% + 4.5% = 104.5%

Multiplier = 1.045 Current Value =

9

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Ex. 2 Lauren bought some shares in a company 3 years ago for £600. In the first year they appreciated by 2.4%. In the second year by 3.7% and in the third year by 4.8%. What are the shares now worth ?

Year 1 multiplier = 1.024

600 x 1.024 =

Year 2 multiplier = 1.037

x 1.037 =

Year 3 multiplier = 1.048

x 1.048 =

Depreciation Remember The starting

percentage at the

beginning of a calculation is

100%.

This time we are going down from 100%

Depreciation Rate

%

Multiplier

5%

(100% - 5%)

95%

0.95

3%

(100% - 3%)

97%

0.97

12%

(100% - 12%)

88%

0.88

96.6%

0.966

93.5%

0.935

3.4% 1

6 % 2

(100% - 3.4%)

1

(100% - 6 2 % )

The effect of these multipliers is to reduce values. 10

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Examples Ex. 3 The value of Tony's car when he bought it was £12000. In its first year its value depreciated by 32%. In its second year its value depreciated by 8.4%.

What was it worth after 2 years? Year 1 multiplier = 0.68 Year 2 multiplier = 0.916

12000 x 0.68 =

x 0.916 =

Ex.4 An antique cost Pat £450 but he managed to sell it a few months later for £610. By what percentage had the antique appreciated.

Multplier =

610

=

450

%

So appreciation = Ex.5 In the recent recession the value of a house went down from £190000 to £167000. Express this depreciation as a percentage of the original value.

Multiplier =

167000

=

190000

%

So depreciation =

Exercise 3

Page 6

All questions

11

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Significant Figures When doing calculations we often have to round our answers to a number of significant figures. ( sig. figs )

Round to 1 sig fig in each case.

3246 134 12398 34 24.6 remember 0,1,2,3,4 leave 5,6,7,8,9 round up

Round to 2 sig figs in each case.

3246 134 12398 345 2.56

12

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

Round to 3 sig figs in each case.

3246 32.876 12398 1298.34 1.325

Exercise 4 Page 8 Q 1 - 4 le

mp xa

e

Albert deposits £400 for 3 years in his Investment Account at a rate of 5% in year 1, 10% in year 2 and 8% in year 3. How much will he have in the account after the 3 years? Give your answer correct to 3 sig. figs.

Yr. 1 Interest 5% of £400 = £20 £420 in account Yr. 2 Interest 10% of £420 = £42 £462 in account Yr. 3 Interest 8% of £462 = £36·96 £498·96 in account £499 in account (answer correct to 3 sig. figs.)

Exercise 5 Page 9 Q 1 -8

Check-up page 11

End of Unit 1.1 Percentages 13

INT 2 1.1 Percentages Notebook.notebook

June 25, 2011

14