Money Income Tax Banks & Building Societies Savings and Interest Compound Interest Appreciation & Depreciation Working Backwards

MoneyMoney

Income Tax

Banks & Building Societies

Savings and Interest

Compound Interest

Appreciation & Depreciation

Working Backwards

21 Apr 202321 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Understand the term weekly Understand the term weekly monthly and annual salary. monthly and annual salary.

1. To explain how to work out weekly, monthly and annual salary / wage.

2.2. Calculate weekly, monthly Calculate weekly, monthly and annual salary.and annual salary.

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w.m

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.com

Wages & SalariesWages & Salaries


1. To explain how to work out Income Tax calculations.

1.1. Understand the term Understand the term Income Tax.Income Tax.

2.2. Calculate Income Tax for a Calculate Income Tax for a given salary.given salary.

Income TaxIncome Tax

If your income in a tax year is below a certain value you do not pay tax. The tax allowance is made up of a personal allowance plus other special allowances.

Membership of professional

bodies

Special clothing

equipment


Taxable incomeTaxable income Rate of TaxRate of Tax

Up to £4745Up to £4745 0%0%

£0 - £2020 £0 - £2020 10%10%

£2020 - £31 400£2020 - £31 400 22%22%

Over £31 400Over £31 400 40%40%


Taxable Rates for 2004 / 05


Calculate David’s income tax if he earns £27 000 a year.

Personal allowance £4745

Taxable Income £27 000 – £4745 = £22 255

Tax @ 10% = 10% of £2020 = £202

£4653.70

Tax @ 22% = 22% of ( £22 255 - £2020)


Up to £4745Up to £4745 0%0%

£0 - £2020 £0 - £2020 10%10%

£2020 - £31 400£2020 - £31 400 22%22%

Over £31 400Over £31 400 40%40%

= 22% of £20 235 = £4451.70

Total Income tax = £202 + £4451.70 =


Lauren, a successful business woman earns £70 000.What is her total tax paid and her income after tax.

Personal allowance £4745

Taxable Income £70 000 – £4745 = £65 255

Tax @ 10% = 10% of £2020 = £202

£20 207.60

Tax @ 22% = 22% of ( £31 400 - £2020) = £6463.60


Up to £4745Up to £4745 0%0%

£0 - £2020 £0 - £2020 10%10%

£2020 - £31 400£2020 - £31 400 22%22%

Over £31 400Over £31 400 40%40%

Total tax = £202 + £6463.60 + 13 542 =

Tax @ 40% = 40% of ( £65 255 - £31 400) = £13 542


£20 207.60


Up to £4745Up to £4745 0%0%

£0 - £2020 £0 - £2020 10%10%

£2020 - £31 400£2020 - £31 400 22%22%

Over £31 400Over £31 400 40%40%

Total tax = £202 + £6463.60 + 13 542 =

= £49 792.40

Income after tax = £70 000 - £20 207.60


1.1. To know the meaning of To know the meaning of the term simple interest.the term simple interest.

1. To understand theterm simple interest and compound interest.

2.2. To know the meaning of To know the meaning of the term compound the term compound interest.interest.

Savings & InterestSavings & Interest

3.3. Know the difference Know the difference between simple and between simple and compound interest.compound interest.

99

Just working out

percentagesSimple InterestSimple Interest

I have £400 in the Bank. At the end of each year I receive 7% of £400 in interest. How much interestdo I receive after 3 years. How much do I now have?

1010

I nterest = 7 ÷ 100 × 400 = £28

After 3 years interest is 3 x £28 = £84.

Total in bank is = £400 + £84 = £484

Savings & InterestSavings & Interest


1.1. To know when to use To know when to use compound formula.compound formula.

1. To show how to use the compound formula for appropriate problems.

2.2. Solve problems Solve problems involving compound involving compound formula.formula.

1111

Compound InterestCompound Interest

Compound InterestCompound InterestInterest calculated on

new value every year

Real life Interest is not a fixed quantity year after year. One Real life Interest is not a fixed quantity year after year. One year’s interest becomes part of the next year’s amount. year’s interest becomes part of the next year’s amount. Each year’s interest is calculated on the amount at the Each year’s interest is calculated on the amount at the start of the year.start of the year.

Example

Daniel has £400 in the bank. He leaves it in the bank for 3 Daniel has £400 in the bank. He leaves it in the bank for 3 years. The years. The interest is 7%interest is 7% each year. Calculate the simply each year. Calculate the simply interest and then the interest and then the compound interestcompound interest after 3 years. after 3 years.

Principal value

1212

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

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 = £32.06Amount = £457.06 + £32.06 = £490.02

Compound is £490.02 - £400 = £90.02Simple Interest is only £84

Interest = 7% of £400 = £28

3 x 28 = £84

Simple Interest

Interest calculated on

new value every year

1313


Easier MethodEasier Method

1414

n

100

%1IV

n = period of timeDays, months years

± = increase or decrease

I = initial value

V = Value

IMPORTANT

Can only use this when percentage

is fixed

This is called the multiplier.


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

V= 400 x (1.07)3 =

£490.02

1515

n

100

%1IV

n = 3

± = increase 1+0.07=1.07I =400



1.1. To know the terms To know the terms appreciation and appreciation and depreciation.depreciation.

1. To understand the terms appreciation and depreciation.

2.2. Show appropriate Show appropriate workingworkingwhen solving problems when solving problems containing appreciation containing appreciation and depreciation.and depreciation.

Appreciation & DepreciationAppreciation & Depreciation

1616

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

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

1717


Average house price in Ayr has appreciated by 79% over Average house price in Ayr has appreciated by 79% over past 10 years.past 10 years.

If you bought the house for £64995 in 1994 how much If you bought the house for £64995 in 1994 how much would the house be worth now ?would the house be worth now ?

Appreciation Appreciation = 79% x £ 64995= 79% x £ 64995= 0.79 x £64995= 0.79 x £64995

= = £ 51346.05£ 51346.05New value New value = Old Value + Appreciation= Old Value + Appreciation

= £64995 + £51346.05= £64995 + £51346.05= = £ 116341.05£ 116341.05

Just working out

percentages

1818

Quicker MethodEasier

1.79 x 64995= £116341.05

1919

A Mini Cooper cost £14 625 in 2002A Mini Cooper cost £14 625 in 2002

At the end 2003 it At the end 2003 it depreciateddepreciated by 23% by 23%

At the end 2004 it will depreciate by a further 16%At the end 2004 it will depreciate by a further 16%

What will the mini cooper worth at end 2004?What will the mini cooper worth at end 2004?

End 2003 End 2003

Depreciation Depreciation = 23% x £14625= 23% x £14625

= 0.23 x £14625= 0.23 x £14625

= £3363.75= £3363.75

New valueNew value = Old value - Depreciation= Old value - Depreciation

= £14625 - £3363.75= £14625 - £3363.75

= = £11261.25£11261.25


2020

End 2003 End 2003

Depreciation Depreciation = 23% x £14625= 23% x £14625

= 0.23 x £14625= 0.23 x £14625

= £3363.75= £3363.75

New valueNew value = Old value - Depreciation= Old value - Depreciation

= £14625 - £3363.75= £14625 - £3363.75

= £11261.25= £11261.25

End 2004 End 2004

Depreciation Depreciation = 16% x £11261.25= 16% x £11261.25

= 0.16 x £11261.25= 0.16 x £11261.25

= £1801.80= £1801.80

New Value New Value = £11261.25 - £1801.80= £11261.25 - £1801.80

= £9459.45= £9459.45



1.1. To understand the process To understand the process of work backwards.of work backwards.

1. To understand how to work backwards to find original price.

2.2. Solve problems using Solve problems using backwards process.backwards process.

Work BackwardsWork Backwards

2121

Example 1

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

Price before is 100% : £800 x 100 = £80 000

£88 000 110 = £8001 % :

100 % + 10 % = £88 000Deduce from question :

110 % = £88 000We have :

2222


Example 2

The value of a car depreciated by 15%. It is now valuedat £2550. What was it’s original price.

Price before is 100% : £30 x 100 = £3 000

£2 550 85 = £301 % :

100 % - 15 % = £2 550Deduce from question :

85 % = £2 550We have :

2323


Documents

Money Income Tax Banks & Building Societies Savings and Interest Compound Interest Appreciation & Depreciation Working Backwards