Thinking of buying a bike?Thinking of buying a bike?

Brand New

Price: £1999.00

For those who love living in style. Pleasurable and effortless riding is assured

with automatic transmission and electric start. The well shaped, wide saddle is made

to comfortably host both rider and passenger, while the chrome-plated

handgrip is a stylish addition to the Vespa as well as being functional for the pillion

rider. Discover the unique accessories that highlight the scooters functional aspects as well as its stylishness such as the elegant

and roomy top case with a design that immediately recalls the shape and the

colour of the vehicle, and the new Vespa helmets in matching colours.

Try theTry the VESPA LX 50 2TVESPA LX 50 2T

But can you afford

it?

Can you afford it?Can you afford it?You have £50 per month disposable income which you can put towards your dream machine.

Using the information below and the loan calculator, decide whether you can afford the bike and how long it will take to pay it off?

Brand New

Price: £1999.00

VESPA LX 50 2TVESPA LX 50 2TInvestigate alternative loan offers

on the internet

Taking out a loan?Taking out a loan?

What must you consider?

Loan Loan

amountamount

How much do you need to borrow?

How much do you need to borrow?

Repayment

Repayment periodperiodHow long is the loan for?

How long is the loan for?

Monthly

Monthly

repayme

repayme

ntsnts

How much can you afford to pay

How much can you afford to pay

back each month?

back each month?

Interest Interest (APR)(APR)How much will the lender make?

How much will the lender make?

So how does one affect the other?

So how does the APR affect the So how does the APR affect the monthly repayments?monthly repayments?

InvestigateInvestigate

What is APR? An illustrated example

Click loan illustration for up to date examples

Are you financially astute?Are you financially astute?Thinking as a banker and given the details

below, how much would the ‘fixed’ rate monthly payments need to be to ensure the loan was paid off in time?

APR: 8.7%

Payment Period: 48 months

Loan amount: £15000

APRAPR

‘With the APR calculation the interest changes each year. It is worked out as a percentage of the amount you still owe. After the end of the first year you have paid some of the loan back so your loan has been reduced. Each year the amount of money you owe reduces, so you pay less and less interest.’

‘The letters APR stand for "Annual Percentage Rate" and provide an indication of how expensive a loan is. The APR tells you the rate at which you will be charged interest.’

‘The Annual Percentage Rate is calculated on the amount outstanding, which is reducing each year; because you are paying the loan back on a regular basis, the interest payment you make reduces.’

Taken from www.teamtechnology.co.ukBack

An ExampleAn Example

Back Number Crunching Calculations

So why is the APR different from the total interest paid?

1 £5,000.00 £5,030.22 £30.22 £154.97 £4,875.25

2 £4,875.25 £4,904.73 £29.47 £154.97 £4,749.76

3 £4,749.76 £4,778.47 £28.71 £154.97 £4,623.50

4 £4,623.50 £4,651.45 £27.95 £154.97 £4,496.48

5 £4,496.48 £4,523.66 £27.18 £154.97 £4,368.69

6 £4,368.69 £4,395.09 £26.41 £154.97 £4,240.12

7 £4,240.12 £4,265.76 £25.63 £154.97 £4,110.79

8 £4,110.79 £4,135.64 £24.85 £154.97 £3,980.67

9 £3,980.67 £4,004.73 £24.06 £154.97 £3,849.76

10 £3,849.76 £3,873.03 £23.27 £154.97 £3,718.06

11 £3,718.06 £3,740.54 £22.48 £154.97 £3,585.57

12 £3,585.57 £3,607.24 £21.67 £154.97 £3,452.27

 

24 £1,931.75 £1,943.43 £11.68 £154.97 £1,788.46

 

36 £153.90 £154.83 £0.93 £154.97 -£0.14

Month

Outs

tandin

g loan a

t st

art

of

month

Outs

tandin

g

loan w

ith

inte

rest

Month

ly inte

rest

Month

ly R

epaym

ent

Outs

tandin

g loan

at

end o

f m

onth

Loan:

£5000

APR:

7.5%

Repayment Period:

36 months

Back

Why not £0.00?

Why does the monthly interest decrease yet the

APR remains fixed?

CalculationsCalculations

Example: APR: 7.5%

If no repayments are made within the year, 7.5% will be added onto the original loan.

Since interest is incurred monthly, this must be the equivalent to 7.5% per year (i.e. 107.5% of the loan)

(Monthly interest)12 = 1.075

Monthly interest= 12√1.075 = 1.00604… or 0.6% (approx.)

Back

Up2d8 mathsCredit where credit’s due

Student resource sheets

Month Outstanding loan at the start of month

Outstanding loan with interest

Monthly interest

Monthly repayment

Outstanding loan at the end of month

1 £5 000.00 £5 030.22 £30.22 £154.97 £4 875.25

2 £4 857.25 £4 904.73 £29.47 £154.97 £4 749.76

3 £4 749.76 £4 778.47 £28.71 £154.97 £4 623.50

4 £4 623.50 £4 651.45 £27.95 £154.97 £4 496.48

5 £4 496.48 £4 523.66 £27.18 £154.97 £4 368.69

6 £4 368.69 £4 395.09 £26.41 £154.97 £4 240.12

7 £4 240.12 £4 265.76 £25.63 £154.97 £4 110.79

8 £4 110.79 £4 135.64 £24.85 £154.97 £3 980.67

9 £3 980.67 £4 004.73 £24.06 £154.97 £3 849.76

10 £3 849.76 £3 873.03 £23.27 £154.97 £3 718.06

11 £3 718.06 £3 740.54 £22.48 £154.97 £3 585.57

12 £3 585.57 £3 607.24 £21.67 £154.97 £3 452.27

24 £1 931.75 £1 943.43 £11.68 £154.97 £1 788.46

36 £153.90 £154.83 £0.93 £154.97 -£0.14

Example

Given the details above, how much would the ‘fixed’ rate monthly

payments need to be to ensure the loan was paid off on time?

APR: 8.7%Payment period: 48 months

Loan amount: £15 000

Up2d8 mathsCredit where credit’s due

Teacher Notes

Credit where credit’s dueIntroduction: As the successful management of personal finances becomes increasingly important in light of the recent

credit crunch, is there a need tounderstand the terms and conditions when selecting and taking on a personal loan? Content objectives: • calculate an original amount when given the transformed amount after a percentage change; use calculators for reverse

percentage calculations by doing an appropriate division• use inverse operations, understanding that the inverse operation of raising a positive number to power n is raising the

result of this operation to power • know that   =  and   =  for any positive number n• break down substantial tasks to make them more manageable; represent problems and synthesise information in

algebraic, geometrical or graphical form; move from one form to another to gain a different perspective on the problemProcess objectives: These will depend on the amount of freedom you allow your class with the activity. It might be worth considering how you’re

going to deliver theactivity and highlighting the processes that this will allow on the diagram below.

Activity: Within this unit, students are asked to consider how they might borrow money to buy a scooter. They are asked tolook at existing loan offers that are available and decide whether they are suitable, affordable and value for money. There isalso an opportunity for students to investigate the ways in which loans are calculated, how the interest is repaid and theimplications of changing certain variables (e.g. length of loan, loan amount, APR).

Differentiation: In addition to the notes provided, much information and explanation is available on the internet. You may decide to change the level of challenge for your group. To make the task easier you could consider:• Inputting given variables within an online ‘loan calculator’ to investigate the monthly repayment costs.• Finding and comparing existing loan offers advertised on the internet.• Investigating the effect changing one variable (e.g. length of loan) has on the monthly repayments.To make the task more complex you could consider• Investigating how the equivalent monthly interest rate can be calculated from a given APR• Changing each variable (i.e. APR, loan amount, length of loan), investigating the effect it has on the monthly repayments and

the total interest incurred.• Investigating possible ‘hidden’ costs/extras charged by banks.• How the students’ understanding of APR may be applied to available repayment mortgage deals. What are the advantages

and disadvantages ofincreasing/decreasing the length of your mortgage?

This resource is designed to be adapted to your requirements.

Outcomes: You may want to consider what the outcome of the task will be and share this with students according to their ability. This could be:

• Explaining the details of a loan they could take out to buy a scooter• An advertisement for a competitive made up loan, illustrating the necessary terms and conditions• Examples of different available loans which students think are good value for money and bad value for money with reasons• A spreadsheet/graph illustrating the correlation between monthly repayments and another variable (e.g. APR, loan amount,

length of loan)

Working in groups: This activity lends itself to paired or small group work and, by encouraging students to work collaboratively, it is likely that you will

allow them access to more of the key processes than if they were to work individually.You will need to think about how your class will work on this task. Will they work in pairs, threes or larger groups? If pupils are not

used to working ingroups in mathematics you may wish to spend some time talking about their rules and procedures to maximise the effectiveness

andengagement of pupils in group work (You may wish to look at the SNS Pedagogy and practice pack Unit 10: Groupwork for

guidance). You may wish toencourage the groups to delegate different areas of responsibility to specific group members.

Assessment: You may wish to consider how you will assess the task and how you will record your assessment. This could include developing the

assessment criteria with your class. You might choose to focus on the content objectives or on the process objectives. You might decide that this activity

lends itself to comment only marking or to student self-assessment.

Are you fi nancially astute?Are you fi nancially astute?

Given the details below, how much would the ‘fixed’ rate monthly payments need to be to ensure the loan was paid off in time?

APR: 8.7%

Payment Period: 48 months

Loan amount: £15000

APRAPR

‘With the APR calculation the interest changes each year. It is worked out as a percentage of the amount you still owe. After the end of the first year you have paid some of the loan back so your loan has been reduced. Each year the amount of money you owe reduces, so you pay less and less interest.’

‘The letters APR stand for "Annual Percentage Rate" and provide an indication of how expensive a loan is. The APR tells you the rate at which you will be charged interest.’

‘The Annual Percentage Rate is calculated on the amount outstanding, which is reducing each year; because you are paying the loan back on a regular basis, the interest payment you make reduces.’

Taken from www.teamtechnology.co.ukBack

An ExampleAn Example

Back

- £0.14£154.97£0.93£154.83£153.9036

£1,788.46£154.97£11.68£1,943.43£1,931.7524

£3,452.27£154.97£21.67£3,607.24£3,585.5712

£3,585.57£154.97£22.48£3,740.54£3,718.0611

£3,718.06£154.97£23.27£3,873.03£3,849.7610

£3,849.76£154.97£24.06£4,004.73£3,980.679

£3,980.67£154.97£24.85£4,135.64£4,110.798

£4,110.79£154.97£25.63£4,265.76£4,240.127

£4,240.12£154.97£26.41£4,395.09£4,368.696

£4,368.69£154.97£27.18£4,523.66£4,496.485

£4,496.48£154.97£27.95£4,651.45£4,623.504

£4,623.50£154.97£28.71£4,778.47£4,749.763

£4,749.76£154.97£29.47£4,904.73£4,875.252

£4,875.25£154.97£30.22£5,030.22£5,000.001

Mon

th

Out

stan

ding

loan

at

star

t of

mon

th

Out

stan

ding

loan

w

ith in

tere

st

Mon

thly

inte

rest

Mon

thly

Rep

aym

ent

Out

stan

ding

loan

at

end

of

mon

th

Loan:

£5000

APR:

7.5%

Repayment Period:

36 months

Back

Why not £0.00?

CalculationsCalculations

Example: APR: 7.5%

I f no repayments are made within the year, 7.5% will be added onto the original loan.

Since interest is incurred monthly, this must be the equivalent to 7.5% per year (i.e. 107.5% or the loan)

(Monthly interest)12 = 1.075

Monthly interest= 12√1.075 = 1.00604… or 0.6% (approx.)

Back

Thinking of buying a bike?Thinking of buying a bike?

Brand New

Price: £1999.00

For those who love living in style. Pleasurable and effortless riding is assured

with automatic transmission and electric start. The well shaped, wide saddle is

made to comfortably host both rider and passenger, while the chrome-plated

handgrip is a stylish addition to the Vespaas well as being functional for the pillion

rider. Discover the unique accessories that highlight the scooters functional aspects as well as its stylishness such as the elegant

and roomy top case with a design that immediately recalls the shape and the

colour of the vehicle, and the new Vespahelmets in matching colours.

Try theTry the VESPA LX 50 2TVESPA LX 50 2TCan you afford it?Can you afford it?

You have £50 per month disposable income which you can put towards your dream machine.

Using the information below and the loan calculator, decide whether you can afford the bike and how long it will take to pay it off?

Brand New

Price: £1999.00

VESPA LX 50 2TVESPA LX 50 2TI nvestigate alternative

loan off ers on the internet

So how does the APR eff ect the So how does the APR eff ect the monthly repayments?monthly repayments?

I nvestigateI nvestigate

What is APR? An illustrated example

Click loan illustration for up to date examples

Probing questions: Initially students could brainstorm issues to consider. You may wish to introduce some points into the discussion which might include:-Why do people take out loans?-When taking out a loan, what must you consider?-Who benefits from taking out a loan?-Why are banks or other financial institutions keen to offer loan facilities ?-What happens if you stop repaying a loan?-How do interest rates on loans compare with interest rates on savings?-Who would you go to when taking out a loan? Would it be advantageous to shop around?-When comparing loans, how can you tell which one is most suited to you?You will need The PowerPoint display which you might read through with your class to set the scene at the beginning of the activity. There are nine slides.

The first and second slides set the scene in the context of buying a scooter.

The third slide asks what considerations must be made when taking out a loan and how one affects the other.

The fourth slide shows comparative loans with varying APR. There are links to additional supporting slides:

The fifth slide show gives a specific loan conditions and a related task.

Taking out a loan?Taking out a loan?

What must you consider?

Loan am

ount

Loan am

ount

How much do you need to borrow?

How much do you need to borrow?

Repayment period

Repayment periodHow long is the loan f or?

How long is the loan f or?

Monthly

Monthly

repayments

repayments

How much can you aff ord to pay back

How much can you aff ord to pay back

each month?

each month?

I nterest (APR)

Interest (APR)How much will the lender make?

How much will the lender make?

So how does one affect the other?

If required, there are formatted spreadsheets available to assist students in the

investigation of how loans are calculated:

• 24 months Repayment Calculator

• 36 months Repayment Calculator

• 48 months Repayment Calculator

• 60 months Repayment Calculator