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A Note on Varying Rates of Interest

Published online by Cambridge University Press:  03 October 2014

W. F. Scott
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Synopsis

Let us suppose, for the purpose of calculating premium rates, that interest rates will not fall below those of the straight lines from their present value io to in in n years' time (in < io), thereafter remaining constant at in. On the basis of this assumption we derive formulae for the (minimum) effective rates of interest on single and annual premium contracts of term m years (m ≤ n, or m > n) and give examples in which gross interest rates fall from 8%, 9%, 10%, 11%, to 4½% in 40 years' time, and other examples. We conclude with a discussion of modifications to the term of the contracts which enable our results to be used for pure endowments, with-return endowments, endowment assurances, deferred annuities and other policies in life assurance and pensions business, and we mention some objections to our methods.

Our thanks are due to C. M. Stewart, F.I.A., F.S.S., for suggesting some improvements to this note.

Type
Research Article
Information
Transactions of the Faculty of Actuaries , Volume 34 , 1973 , pp. 443 - 449
Copyright
Copyright © Institute and Faculty of Actuaries 1973

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References

1.Donald, D. W. A.Compound Interest and Annuities-Certain, second edition. C.U.P.Google Scholar
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3.Lidstone, G. J.Note on an Extension of Stoodley's Formulae for valuation at a varying rate of interest. T.F.A., 14, p. 176.Google Scholar
4.Cavaye, C. M. and Springbett, T. M.Actuarial Note on the Calculation of Premium Rates using a Decreasing Rate of Interest and allowing for the Benefits of Immunisation. T.F.A., 28, p. 308.Google Scholar