Parents offer their 16yo dd a generous (but not ridiculously generous) allowance of several hundred pounds per month. They will continue to look after all costs associated with school and family, but she will be responsible for controlling her own budget and spending on travel, clothes, entertainment etc out of the allowance. They offer it as a gift/reward, not as a brush-off.
The 16yo refuses because the idea frightens her.
What would you do? How do you respond?