A few problems to get you started:
- http://www.uio.no/studier/emner/sv/oekonomi/ECON4120/v09/undervisningsmateriale/mat2v09-1.pdf . In problem 4, you may also solve the equality obtained by replacing "=" by ">". Test by plugging in values x=1/2, x=3/2 and x=5/2 -- did you forget something?
- Let r>0 be a constant and define f(z) = (1+r/z)z for z>0. Show that f is an increasing function -- that is, that effective interest rate is higher the more often interest is accumulated. Proceed as follows:
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You may want to consider g(z) = ln f(z) = z ln(1+r/z) instead of f; point out that f is increasing if and only if g is (at least whenever the logarithm is defined).
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Find g'(z) and point out that g'(z) tends to 0 when z tends to infinity.
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Find g''(z) and point out that it is negative.
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What do the latter two points tell you about the sign of g'(z)?