What type of loan pays a rate of interest below market value but includes a payment to the lender of some form of appreciation?

The correct choice is equity participation. This type of loan arrangement allows a borrower to secure financing at a lower interest rate than current market rates. In exchange for this favorable interest rate, the lender participates in the appreciation of the asset—typically through a share of the future profits or increased value of the property. This arrangement aligns the interests of both the borrower and lender, as both parties benefit from the property's growth.

Equity participation is often found in commercial real estate financing, where lenders are looking not just for standard interest payments but also for a return that reflects the potential appreciation in the property's value over time. The anticipation of future cash flows, bolstered by a partnership-like structure, creates an incentive for both parties to ensure the property performs well.

Other types of loans listed do not include the characteristic of appreciation payments that equity participation offers; variable-rate loans only change interest rates over time based on market variables, leasehold pertains to property rental agreements rather than loans, and wraparound loans involve a second mortgage that wraps around an existing loan but does not inherently include appreciation provisions in the same manner.