By David Lovelock

ISBN-10: 0387344322

ISBN-13: 9780387344324

This is an undergraduate textbook at the uncomplicated features of private discount rates and making an investment with a balanced mixture of mathematical rigor and fiscal instinct. It makes use of regimen monetary calculations because the motivation and foundation for instruments of uncomplicated genuine research instead of taking the latter as given. Proofs utilizing induction, recurrence family members and proofs via contradiction are coated. Inequalities similar to the Arithmetic-Geometric suggest Inequality and the Cauchy-Schwarz Inequality are used. simple themes in chance and information are provided. the scholar is brought to parts of saving and making an investment which are of life-long functional use. those contain reductions and checking bills, certificate of deposit, scholar loans, charge cards, mortgages, trading bonds, and purchasing and promoting stocks.

The ebook is self contained and obtainable. The authors stick with a scientific development for every bankruptcy together with quite a few examples and workouts making sure that the coed offers with realities, instead of theoretical idealizations. it truly is compatible for classes in arithmetic, making an investment, banking, monetary engineering, and comparable topics.

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**Additional resources for An Introduction to the Mathematics of Money: Saving and Investing**

**Sample text**

Solve this for Sn . (See p. 36. The geometric mean of the non-negative numbers a1 , a2 , . . , an is (a1 a2 · · · an )1/n . Prove that the IRR of n successive annual investments with rates i1 , i2 , . . , in compounded m1 , m2 , . . , 1 + i1 mn mn . 37. Show that the IRR that corresponds to a nominal rate i(m) compounded m times a year does not depend on the number of years it is invested. 38. Show that the IRR that corresponds to a simple interest investment rate of i depends on the number of years it is invested.

If the annual eﬀective rate is ieﬀ and the annual tax rate, t, is constant, then the after-tax future value of P0 after n years is Pn = P0 (1 + ieﬀ − ieﬀ t)n . 4) We now introduce the after-tax rate of interest, itax , which is the after-tax annual rate at which P0 grows to Pn when compounded annually at that rate. 4), we have 1 + itax = 1 + ieﬀ − ieﬀ t. This can be rewritten as itax = ieﬀ − ieﬀ t = ieﬀ (1 − t). 1. 1 on p. 46 are correct. 2. In what years did the United States experience deﬂation?

Thus, as time goes by, our money buys less and less. • If iinf = ieﬀ , then {Pn } is a constant sequence. As time goes by, our money buys the same amount even though we are earning interest. • If iinf < ieﬀ , then {Pn } is an increasing sequence for which limn→∞ Pn = ∞. Thus, as time goes by, our money buys more and more. • We introduce the real rate of interest, ireal , which is the annual rate at which P0 grows to Pn when interest is compounded annually at ieﬀ adjusted for inﬂation. Thus, Pn = P0 (1 + ireal )n .