Social Arithmetic

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Utility Bills

Telephone, Gas and Electricity bills usually have a standing charge, plus
a cost for each unit used. VAT is payable on top of this.

Number of units used = Present reading – Previous reading
Total charge for units = Number of units used x Cost per Unit
VAT is payable on the whole bill

Loans

Secured Loans – If you default on payments, your house is at risk.
Unsecured Loans – The goods bought are yours. Your house is safe.
Hire Purchase – The goods bought are not yours until the last payment has been made.
Mortgages – Secured loans for Houses, Ships, etc.

Example

Joe Bloggs wishes to borrow £10,000.
Which of the following options is the cheapest way to borrow ?

loan2

fred

The cheapest way with EasyLoan costs £17,343 for 15 years .
The cheapest way with Loans R us costs £11,122.56 for 3 years (unprotected.)

Fred’s Finance costs

Cheapest method is with Loans R us for 3 years (unprotected.)

Hire Purchase (HP)

With Hire Purchase, a deposit is paid and is then followed by a set amount of monthly repayments. Sometimes, a final payment is also made.

The goods are not yours until the final payment is made.

Example

A television costs £600 cash.
It is available on HP for a 10% deposit
followed by 36 monthly instalments of £ 15.75

How much cheaper is to pay cash ?

It is £27 cheaper to pay by cash.

Car Finance

car

There are a few options available when buying a car :

Cash: You buy the car outright.

Car loans: You buy the car outright and spread the cost over a longer period of time.

Hire Purchase (HP): Spread the cost of the car over several months or years. You'll own the car outright once you've made all payments.

Personal Contract Purchase (PCP): Take out a loan to cover the car's depreciation. You have the option to buy the car at the end of the contract.

Leasing: Personal Contract Hire (PCH) :A long-term car rental contract where the car never actually belongs to you.

Hire Purchase (HP)

Hire Purchase allows you to buy a car without having to pay the full amount upfront. A monthly fee is paid to hire the car, which covers the cost of the car as well as interest charges. The car remains the property of the HP company until the final payment has been made.

Key features of Hire Purchase

Contracts can be up to 5 years long.
The cost can be spread to suit your circumstances.
The car is yours to own at the end of the agreement.
There are no mileage restrictions.
You choose how much deposit you put down at the start of the agreement.

Risks of Hire Purchase

You do not own the car until the final payment is made.
If you fail to make the payments set out in your agreement, your car could be repossessed, and your credit rating may be adversely affected

Deposit

The deposit is the amount you pay upfront at the start of the agreement, and it will determine how much you need to borrow.
The larger your deposit, the less you’ll have to borrow and the smaller your monthly payments will be.

Monthly Payments

Once you’ve chosen the term (length) of your agreement, the amount of the monthly repayments will be spread equally across the months and remain fixed throughout your agreement.

End of Contract

Once you’ve made your final monthly payment, the car is yours to keep or part exchange it for a new car.

Personal Contract Purchase (PCP)

Personal Contract Purchase (PCP) is a way to borrow money to buy a car. You pay back the money every month, and at the end of the contract, you can choose to return the car, upgrade, or make one final payment (Optional Final Payment) to own it.

Key features of Personal Contract Purchase

Monthly payments are kept low as an amount is deferred to the end of the agreement
Flexible options at the end of a contract – keep, upgrade, or return the car.

Risks of Personal Contract Purchase

Each car comes with an agreed mileage limit which must be kept to, otherwise you will be charged an additional excess mileage charge.
If your car is damaged beyond regular wear and tear there is a risk of additional charges.
You do not own the car until you make the final payments at the end of your finance agreement.
If you fail to make the payments set out in your finance agreement, your car could be repossessed, and your credit rating may be adversely affected.

Deposit

The deposit is the amount you pay upfront at the start of the agreement, and it will determine how much you need to borrow.
The deposit ranges from 0 to 35% of the vehicle price.
The larger your deposit, the less you’ll have to borrow and the smaller your monthly payments will be.

Monthly Payments

Your monthly payments will be fixed throughout your agreement and are affected by the amount of your deposit.
A Guaranteed Future Value (GFV) is used to determine how much you’ll have to pay at the end of your finance agreement in order to own the car.

Car Usage

Your PCP agreement will come with rules around car usage that help you avoid any further charges. These will determine how many miles you can drive throughout your agreement.

Leasing, Personal Contract Hire (PCH)

Personal Contract Hire is a finance offer that allows you to hire a car for an extended length of time. You pay a fixed monthly fee to hire the vehicle, and throughout the length (term) of the agreement it is your responsibility to take care of it. You do not own the car and you must return it at the end of the agreement.

Key features of Personal Contract Hire

Contracts offer terms between 24 and 48 months.
You choose how much deposit you put down at the start of the agreement.

Risks of Personal Contract Hire

You must maintain the car’s condition to meet manufacturer guidelines.
If you return the car in poor condition, or exceed the agreed mileage limit , you will be charged an additional fee.
You do not own the car.
If you fail to make the payments set out in your agreement, your car could be repossessed, and your credit rating may be adversely affected.

Initial Rental

The Initial Rental is the amount you pay upfront at the start of the agreement.
The Initial Rental equates to the value of anywhere between 1 to 9 months rentals.

Monthly Rentals

Your monthly rentals will be fixed throughout your agreement, and they are affected by the size of your Initial Rental.
Once you’ve chosen the term (length) of your agreement, the rental amounts will be spread equally across the months.
To help keep the car within the wear and tear guidelines, optional maintenance packages can be added into the monthly rental cost. You will be expected to stick within the pre-agreed mileage limits and if you fail to do so, you will face a fee.

End of Agreement

Once you’ve made your final monthly rental and your agreement has come to an end, it’s time to return your car to the lender.
Upon its return, the car will be assessed for wear and tear against the manufacturer guidelines that were shared with you at the start of the agreement.
If any damage is noted beyond the usual wear and tear, you will face an additional fee.

Insurance

All insurance policies are based on the probability that a certain event will not happen.
The higher the probability is that an event will happen , the higher the insurance premium.

Example

Bodgit Insurance offer house cover at a premium of £3.50 per £1000.
How much does it cost to cover a £189,000 house ?

Bank Interest

Interest is a percentage of the capital that is charged on loans/borrowing money and paid on savings.

Simple Interest

Simple interest gives you a percentage return based purely on your original capital.

Example

Calculate the simple interest on £500 for 3 years at 6% per annum.

Compound Interest

Compound interest uses the interest earned to increase the capital,
thus increasing interest.

Example

Calculate the compound interest on £500 for 3 years at 6% per annum.

If the interest rate per annum doesn't change, a formula can be used
which is based on the starting value (capital),the increased or reduced interest rate and the term of the calculation.

If the calculation is based over years, the mnemonic CR^y can be used:-

Example

Calculate the compound interest on £500 for 3 years at 6% per annum.

The mnemonic CR^y can still be used for monthly payments, but remember to convert the term to months:-

Example

Calculate the compound interest on £500 for 1 year at 0.3% per month.

This can also be used to work out a rough APR (Annual Percentage Rate ) :-

Example

What is the APR for a credit card which charges 1.5% interest per month?

Effective Interest

Also known as AER, Annual Equivalent Rate

This is the true interest rate on a loan that takes compounding into account. It is the figure used to compare loans and investment rates of terms.

Effective Interest Rate = (1 + (Nominal Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods) - 1

aer

where r is the annual effective rate , i is the nominal interest rate ( the stated or quoted rate ) and n is the number of compounding periods per year.

compound periods

The compounding period is important, since it can affect the amount of money earned or owed.

Example

A bank offers a loan with a nominal annual rate of 5%, compounded monthly.

Find the annual effective rate.

The annual effective rate is 5.12%

Example

A bank offers a loan with a nominal annual rate of 5%, compounded semi-annually.

Find the annual effective rate.

semi

The annual effective rate is 5.06%

Example

A bank offers a loan with a nominal annual rate of 5%, compounded daily.

Find the annual effective rate.

daily

The annual effective rate is 5.13%

Nominal interest rate from effective rate of interest

Working backwards

If given an effective rate, or AER, the nominal interest rate can be found by changing the subject of the formula from r to i.

awer3

nominal rate

where i is the nominal interest rate ( the stated or quoted rate ) , r is the annual effective rate and n is the number of compounding periods per year.

Example

What is the annual nominal interest rate for a loan with an AER of 9% compounded monthly ?

nomi