Deferment doesn't mean your payment is $0 per month. It means you have a payment amount (whatever it current is) and you're allowed to skip it. However, as a result, your loan balance will continue to grow.

IBR is a great program. However, IBR for new loans is a 20 year repayment term. IBR for older loans (before 2014), is 25 years. You make payments based on your income every year, at at 25 years, any remaining balance is forgiven.

If your payment amount doesn't cover interest, that just continues to accrue. So a $0 payment will see your loan continue to grow. But remember, you get forgiveness after 20 or 25 years.

Now, here's the catch - currently any debt forgiven under this program is considered taxable income. So, you could face a large tax bill down the road. In other words, if you can afford to make an extra payment - don't. Save the money. You might/will need it.