Airbnb Inc. agreed to pay its new investors interest at a rate of more than 10% and to strengthen its leadership, in return for the $1 billion in additional funding announced Monday, according to people familiar with the matter.

The investors will also get warrants that can be converted into shares with a valuation for the company of $18 billion, a drop of almost half since Airbnb’s last fundraising in 2017, the people said.

The...