Tenn. Code § 35-3-114
All trustees and guardians in this state, unless prohibited, or another mode of investment is prescribed, by the will or deed of the testator or other person establishing the trust, may invest trust funds in their hands, in addition to the investments heretofore authorized, in certificates of deposit of, and savings accounts in, any national or state bank in the United States, including itself if such trustee or guardian is a national or state bank in the United States otherwise qualified, whose deposits are insured by the federal deposit insurance corporation, at the prevailing rate of interest of such certificates or savings accounts. No trustee or guardian shall invest in such certificates of deposit of, or savings accounts in any one (1) bank, an amount from any one (1) fund in the trustee's or guardian's care in excess of such amount as is fully insured as a deposit in the bank by the federal deposit insurance corporation, unless the investment is first approved by a court of competent jurisdiction.
T.C.A. § 35-3-114