The Charitable Lead Annuity Trust, Charitable Remainder Annuity Trust, Grantor Retained Annuity Trust, and Charitable Gift Annuity calculations all need to perform an exhaustion test. This test can be performed using one of two different methods:
The IRS Annuity Factor Method: This is the method that appears to have been used by the IRS in §25.7520-3(b)(2)(v), example 5. It uses published annuity factors to determine when the trust exhausts, and what the payment is in the last period of the trust.
The Exact Method: This method creates the schedule of payments based on the assumption that the trust will grow at a rate equal to the §7520 rate. From the schedule, it is able to determine exactly when the trust exhausts and how much the final payment is.