My research investigates the use and meaning of all solutions (interest rates) to the time value of money equation. The research attempts to understand interest rates that have been ignored by economists for centuries. The time value of money features in many areas of financial economics, and therefore the research has a variety of applications in economic theory, capital budgeting, retail & corporate finance, fixed income mathematics, and behavioural economics.

Some of the research is summarised in the book 'Multiple Interest Rate Analysis' published in January 2014 by Palgrave Macmillan:

'I liked everything about it (except for the title, which gave me no clue about what was inside). If anyone had asked me, I would have guessed that there was nothing very new to be said about present-value equations, but you have certainly showed that conjecture to be wrong. The product of the roots of the present-value polynomial contains interesting and useful information, as the book demonstrates'. Robert M. Solow, Nobel Laureate in Economics (1987), Institute Professor, Emeritus, and Professor of Economics, Emeritus, Massachusetts Institute of Technology.

'When facing complex problems that arise in the real world, one should always remember that real answers to real questions may require imagination. This book gets to the real root of such problems and more.' Peter Carr, PhD, Department Chair, Finance and Risk Engineering, Tandon School of Engineering, New York University.

'This is seminal stuff. The material in this book should have been discovered in the 1930s, 1940s, or 1950s. Instead, it managed to evade capture until very recently. I regret not having had access to this book in the 1980s, when I first worried about these and related issues as a graduate student. I thought at that time that no further resolution existed. So, this book was an eye opener for me. It is difficult to overemphasize the importance of Osborne’s work in finally putting into place that last missing piece of a jigsaw puzzle handed down from generations of previous financial economics researchers. Osborne carefully explains why multiple-interest-rate solutions to TVM equations are important, even those pesky large negative or complex-valued outcomes that other researchers are all too eager to discard.' Timothy Falcon Crack, PhD, Professor of Finance, University of Otago, New Zealand.

A computable document written in Mathematica is available in the Wolfram Demonstrations Project at The document enables dynamic illustrations of many examples in the book.

A recent Tedx talk gives the flavour of the research via one of its many applications (retail finance):

A more general talk is available here:

Various research papers are in SSRN at and in REPEC at PhD thesis is in the Middlesex University research repository at

For recent published research see the section 'Selected Publications'. For working papers and conference presentations see below.

Working papers:

Osborne, Mike (2014) There’s life in the exponential discounting dog yet.

Osborne, Mike (2011) A note on Macaulay’s formula for duration. SSRN.

Osborne, Mike (2011) An essay on the inadequacy of APR as a measure of the cost of consumer credit, and why consumer credit legislation should be revised. SSRN.

Osborne, Mike (2010) On the meaning of internal rates of return and why an internal rate of return is not an investment criterion. SSRN.

Osborne, Mike (2010) The Cambridge controversies in the theory of capital: a solution to the reswitching puzzle. SSRN.

Conference presentations:

Osborne, Mike (2015) Exponential versus hyperbolic discounting: a theoretical analysis. 3rd Conference of the Behavioural Finance Working Group (Queen Mary University London) on Financial Regulation, 11-12 June.

Osborne, Michael and Davidson, Ian (2013) The Cambridge controversies in the theory of capital: contributions from the complex plane. 15th Conference of the Association for Heterodox Economics, London Metropolitan University, 4-6 July.

Osborne, Mike (2011) On the significance of Sraffa's reswitching: some long-standing financial puzzles and their joint resolution. Keynes Seminar, Robinson College, University of Cambridge, 15 February.

Osborne, Mike (2005) A simple, accurate formula for the duration of a portfolio of bonds under a non-parallel shift of a non-flat yield curve. International Conference on Finance, Finance Research Unit, University of Copenhagen, Copenhagen, Denmark, 2-5 September.

Osborne, Mike (2004) On the computation of a new formula for the duration of a bond that yields precise results without the need for convexity and other devices. 53rd Annual Conference of the Midwest Finance Association, Chicago, Illinois, USA, 18-20 March.

Osborne, Mike (2002) A fresh look at the time value of money equation.15th Australasian Finance & Banking Conference, University of New South Wales, Sydney, Australia, December.

Osborne, Mike (2001) On the time value of money equation and its application to risk. In: 3rd International Conference on Money, Investment & Risk, Nottingham Trent University, 1-2 November.

Osborne, Mike (2001) A new approach to interest rate sensitivity using the complex plane. In: Proceedings of the International ICSC Congress on Computational Intelligence: Methods and Applications (CIMA'2001), Advanced Computing in the Financial Markets, University of Wales at Bangor, 19-22 June.

Osborne, Mike (1996) The impact of some market research on the design of a training program for the wholesale financial markets. In: Proceedings: International Conference on `Finance & Banking Training in the Modern World', Moscow, Russia, September.

Early publications (not included in 'Selected Publications'):

Osborne, Mike (1989) On Popper, education and training, Banking and Financial Training, 5(1).

Osborne, Mike (1989) On the marginal cost of a student in the public sector of higher education in the UK, Journal of Further and Higher Education, 13(1).

Osborne, Mike (1984) On the presentation of IS-LM analysis, The Indian Economic Journal, 32(1).

Snowden, Brian and Osborne, Mike (1982) Inflation and unemployment, Chap. 3, What sort of society? Elcock, G. (ed.), Martin Robertson, ISBN 0-85520-524-5.