By David Lovelock

This is an undergraduate textbook at the easy points of non-public discount rates and making an investment with a balanced mixture of mathematical rigor and monetary instinct. It makes use of regimen monetary calculations because the motivation and foundation for instruments of user-friendly actual research instead of taking the latter as given. Proofs utilizing induction, recurrence family members and proofs by means of contradiction are coated. Inequalities equivalent to the Arithmetic-Geometric suggest Inequality and the Cauchy-Schwarz Inequality are used. simple themes in likelihood and records are awarded. the scholar is brought to parts of saving and making an investment which are of life-long functional use. those comprise mark downs and checking money owed, certificate of deposit, pupil loans, charge cards, mortgages, trading bonds, and purchasing and promoting shares. The ebook is self contained and available. The authors persist with a scientific trend for every bankruptcy together with a number of examples and workouts making sure that the coed bargains with realities, instead of theoretical idealizations. it's compatible for classes in arithmetic, making an investment, banking, monetary engineering, and comparable topics.

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**Extra resources for An introduction to the mathematics of money**

**Example text**

693 by the natural logarithm of (1 + i). Not exactly a handy rule of thumb! 1. 3 on p. 16. 2. Tom Kendrick invests $1,000 at a nominal rate of i(1) , leaving the interest at the end of each year to compound. At the end of the fourth year he earned $300 in total interest. Determine i(1) . 1 on p. 10. Which one do you expect to be higher? Explain. 3. We invest $1,000 in an account earning 6% per year for 3 years. What is the net present value of our investment if the nominal interest rate is 5%? 4.

3. What is the rate of inﬂation for the period 1980–2005? The period 1990– 2005? The period 2000–2005? 4. In 1974, Helen Kendrick received 10% interest compounded annually on her savings account. Should she be pleased? What was the real rate of interest? 5. On average, the cost of a college textbook is about $75. How much does it cost 25 years from now (in today’s dollars)—when the children of current freshmen are themselves freshmen—if inﬂation runs at 5%? 6. In January 1970, Hugh Kendrick bought a new Toyota Corolla for $2,000.

6)? 318 is another solution. But this solution does not satisfy 1 + i > 0, so we reject it. 0339 is the only acceptable solution? 35. 7) then we see that this is a polynomial equation of degree 12 in (1+i). 7) to have 12 solutions! In fact, it has only one real solution that satisﬁes 1 + i > 0, which we show shortly. To show this, we turn to the general case, where we have the following net cash ﬂows: 0 C0 Period Cash Flow 1 C1 2 C2 ··· ··· n−1 Cn−1 n , Cn where Ck (k = 0, 1, . . , n) are positive, negative, or zero.

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