Which of the following types of consideration involves giving up an existing right?

The type of consideration that involves giving up an existing right is forbearance of existing rights. In the context of contract law, forbearance refers to the act of refraining from exercising a legal right. This can arise when one party agrees not to pursue a legal claim or enforce a right they hold in exchange for something of value from another party. Essentially, the party who forgoes their right is providing consideration by making a conscious decision to relinquish that right, which is legally recognized as valuable in forming a binding contract.

This concept is critical as it establishes a mutual exchange necessary for a valid contract. Forbearance is often seen in settlement agreements where one party concedes a claim in return for a settlement amount, thus creating a binding agreement through the relinquishment of rights.

The other choices do not fit this definition. Repayment of a loan involves fulfilling an obligation rather than giving up a right. Offering a discount can be seen as a business strategy rather than a legal consideration involving rights. Acceptance of partial payment also pertains to the fulfillment of a debt rather than the surrender of a legal claim or right.