Tenn. Code Ann. § 66-29-137

If property other than money is delivered to the treasurer, the owner is entitled to receive from the treasurer income or gain realized or accrued on the property before the property is sold, including, if applicable, dividends, interest, or other increments. If the property was an interest-bearing demand, savings, or time deposit, the treasurer shall pay interest annually at the average annual rate paid on funds in the state pooled investment fund established under § 9-4-603. Interest begins to accrue when the property is delivered to the treasurer and ends on the date on which payment is made to the owner.