Hire purchase is used when someone cannot afford to buy the item; a deposit is usually paid and the balance is paid over a fixed period of time.

## How Does a Hire Purchase Work?

A customer is usually required to pay a deposit. From there, the interest is charged onto the balance that is owed and this is then divided into equal instalments which are paid over a fixed period of time.

We use the simple interest formula for this calculation.

### Example 1

An electronics company offered a $1,200 television to the purchaser where a deposit of$100 was provided upfront with the balance to be paid over 18 equal monthly instalments. Interest is charged at 12.4% p.a. flat rate.

a) What is the total interest paid?

We need to calculate the balance of the loan first. Write down the information applicable to this calculation.

Price = $1,200$
Deposit = $100$

Use this information to calculate the balance of the loan.

Balance $=$ cash price $-$ deposit
Balance $=1,200 - 100$
Balance $=1,100$

Now write the balance ($P$) and additional information we were provided with- making sure that the rate and time are in the same units.

$P=1,100$
$r=12.4$ p.a.
$T=1.5$ years

Use the simple interest formula to calculate the amount of interest.

$I=\dfrac {PrT}{100}$
$I=\dfrac {1,100\times 12.4\times 1.5}{100}$
$I=204.6$

Total interest paid will be $204.60. b) Calculate the repayment value. First, find the total repayment amount (not including the deposit). Total repayment = interest + principal Total repayment = $204.60+1,100$ Total repayment = $1,304.60$ To calculate the repayment amount, take the total amount and divide it by the number of repayments. Repayment = $\dfrac {1,304.60}{18}$ Repayment =$72.477$The regular monthly instalments are$72.48.

c) What is the total cost of the television?

To find this amount, add the marked price with the interest amount.

Total cost = $1,200+204.60$
Total cost = $1,404.60$

The total cost of the television is \$1,404.60.