The amount you owe, in total, will be capitalized from the interest your loan accrued during the forbearance period. This will raise the over all payoff amount as well as raise your monthly payment slightly. If you want to avoid as much increase as you can, pay what you can afford to pay during the forbearance period.
During the time that your private student loan is in forbearance, see if you can work out a reduced interest rate, lower payment, or possibly even a lower payment with your lender. Your goal should be to help your financial situation for as long as possible so you can avoid the need of further help in the future.