The Home Truths 2012 survey estimates that the average private rent in the district will rise from £437 to £669 by 2020.
That means the average family will be paying £8,703 a in rent annually in the next eight years.
The Federation says years of not building enough homes have led to rising rental and house prices across the county - leaving many families struggling to pay for their home.
National Housing Federation lead manager for the East Midlands Chris Hobson said it is ‘crunch time’ for the housing market.
“A whole generation is now at risk of being priced out of renting a home, let alone buying one and that has a huge impact on people’s lives,” he said.
“Being unable to afford the homes they need stops people from moving for work, and it even deters young couples from starting families.”
He added: “As our national Home Truths report indicates, even working families are becoming more and more reliant on housing benefit to help pay their private rent.”
“It’s clear that the chronic undersupply of new homes across England and the East Midlands need to be tackled now, to ease the financial press for families and Government.”
This week Worksop Guardian readers have spoken out about the issue.
Louise Trow said: “Rents and bills are getting harder and harder to pay every month as they keep going up - yet our wages never do.”
Kylie Price said: “My sister used to rent a house paying £600 a month when their mortgage was £490 - now that is greedy when they are pocketing the rest.”
Jenni Casey added: “I rent out and don’t charge the earth just enough to cover the payment and if we need repairs. It’s more important for me to know I have someone who will look after our property as their own and I’m so glad we have that.”