How to say this, accident?

Well… I had my very first experience of ‘small’ accident. I was driving with mum at the highway to Melling Bridge in Lower Hutt. I had to give way to my right. Then, the car was knocked forward. I nearly hit my head on the windscreen. Mum told me to drive to the nearest parking and had a look at the damage. The car, which hit us from behind, belongs to an old couple. The old man was trembling when he wrote down information and recommended car service centre for repairing the car. Stupid old man, only cause trouble for us. Mum phoned him the other day to tell him about repairing the car and he seem reluctant to pay for the damage. He asked mum to claim insurance. Mum said our insurance assessment is $1500 and we can’t claim insurance. After this incident, I’m a bit scared to drive, because people will just knock into me again and cause trouble. Why can’t they just admit they are wrong and pay for damage? Damn them!