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 ?
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 plans are a form of HP, with the options of
- paying the final payment and keeping the car
- using the final payment as a deposit on a new vehicle (subject to the mileage and condition of the car)
- not paying the final payment and walking away.
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 CRy can be used:-
Example
Calculate the compound interest on £500 for 3 years at 6% per annum.
The mnemonic CRy 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.
where i is the nominal interest rate ( the stated or quoted rate ) and
n is the number of compounding periods per year
Example
A bank offers a loan with a nominal annual rate of 5%, compounded monthly.
The annual effective rate is 5.11%
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.
so
Example
What is the annual nominal rate for an annual effective rate of 9% ?
The annual nominal rate is 8.6% , which is a monthly interest rate of 8.6% ÷ 12 = 0.7166666 = 0.72%
APR ( Annual Percentage Rate )
This is the interest rate paid each year on an outstanding loan amount.
It includes charges and fees - but does not include compounding.
Foreign Exchange
Converting currency is a form of applied ratio.
Converting into another currency
Examples
Fred wishes to convert £150 into US dollars.
The exchange rate is £1 = $1.67, with no commission.
How many dollars does he get ?
No. of dollars =£150 x $ 1.67 = $250.50
Using the rule of 3
Converting back
Fred wishes to convert $75 back into pounds sterling.
The exchange rate is still £1 = $1.67, with no commission.
How much does he get ?
Amount of pounds sterling =$ 75 รท $150 = £ 44.91
Using the rule of 3
When Joe converts $150 into Euros, he receives € 108.09
There was no commission. What was the exchange rate ?
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© Alexander Forrest