Bernie lives in Richmond, VA. On February 1, he puts an ad in his local newspaper, advertising his 2006 Ford Fusion for sale for a $13,500 asking price. After waiting for a few weeks with no offers, on March 1, Vivian calls him and offers to purchase the vehicle for $12,000.

Bernie is a bit disappointed by the lack of interest and by Vivian's low offer, but he realizes that there might not be much better offers waiting for him. He invites Vivian to meet on March 5 to complete the negotiation and transaction.

When Vivian shows up at Bernie's house on March 10, she tells Bernie, after some negotiation, that she's willing to pay $12,500 for the car; but that she needs another three weeks to raise the money. Bernie agrees to wait, but only if Vivian will put down a deposit of $1,000. Vivian agrees and Bernie hastily drafts a one page agreement.

Because Bernie wants to keep his options open in case he gets a better offer, he puts the following language into the agreement:

Bernie agrees to sell his 2006 Ford Fusion to Vivian for $12,500 and Vivian agrees to purchase the same for such price. The transaction shall take place no later than March 31.

In the event that the seller breaches this agreement, the seller must refund the purchaser's deposit, but the parties shall be limited to this remedy and only this remedy.

In the event that the buyer breaches this agreement, the seller may keep the buyer's deposit, but the seller shall be limited to this remedy and only this remedy.

Vivian reads and signs the agreement and gives Bernie a check for $1,000.

However, two weeks later, Vivian realizes that she's not going to come up with the $12,500 to pay for the car. So, on March 24, she calls Bernie to tell him that she's pulling out of the deal. Bernie says, "Fine, but I'm keeping the deposit in accordance with our agreement."

Vivian sues for her $1,000 deposit back, claiming that there was no mutuality of consideration for the agreement and that the contract was therefore void.

Under applicable law, is Vivian correct or may Bernie keep the deposit? Why?