Annuities can be purchased with either pre-tax or after-tax dollars. A non-qualified annuity is one that has been purchased with after-tax dollars. A qualified annuity is one that has been purchased with pre-tax dollars. Qualified plans include 401(k) plans and 403(b) plans. Only the earnings of a non-qualified annuity are taxed at the time of withdrawal, not the contributions, as they are after-tax money.