A hire purchase agreement is a type of lease agreement which contains an option to purchase. An initial deposit is normally paid, the amount of which can vary significantly. The outstanding balance will then be paid off in monthly instalments.
Ownership passes after all the instalments have been made and the hirer exercises the option to purchase the goods. The option to purchase is normally a nominal fee which has no bearing on the market value of the goods. This is the key difference between hire purchase and contract purchase.
In the latter, the purchase fee is normally an optional balloon rental which reflects the market value of the goods at the time it becomes available for exercise (the equivalent of the residual value in an operating lease). You either pay it, refinance it or return the asset.
In the case of a hire purchase agreement, the instalments (even if it includes a contractual balloon instalment) amortise the balance outstanding down to zero. The instalments under contract purchase amortises the balance down to the uncontracted balloon.