Description: In this paper, David H. Berne demonstrates mathematically how insurance and annuity premiums can be expressed as weighted averages of compound interest functions. These concepts are expanded on in the paper and discussion. The author noted his approach was to demonstrate the averaging process that goes into the development of actuarial present values, and to provide a new look at the meaning and use of weighted averages. From the 1961 Transactions Vol. 13, No. 36 AB.