Generalized annuities and assurances, and their inter-relationships
- 1 September 1984
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Institute of Actuaries
- Vol. 111 (3) , 555-564
- https://doi.org/10.1017/s0020268100041883
Abstract
By the definition of generalized assurances and annuities, the relation 1 = Ās + δās is shown to be the simplest member of a family of relations in which the present value of the capital and interest repayments is equated to the original amount of a loan. When the force of interest is constant over time, the relation takes the simple form above, but when the force is a polynomial in time, the interest payments become a series of annuities, the payments on which increase over time at different rates.Keywords
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