By David Lovelock

This is an undergraduate textbook at the easy features 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 hassle-free actual research instead of taking the latter as given. Proofs utilizing induction, recurrence family members and proofs through contradiction are lined. Inequalities equivalent to the Arithmetic-Geometric suggest Inequality and the Cauchy-Schwarz Inequality are used. simple subject matters in chance and statistics are awarded. the scholar is brought to components of saving and making an investment which are of life-long useful use. those contain reductions and checking money owed, certificate of deposit, pupil loans, charge cards, mortgages, trading bonds, and purchasing and promoting stocks.

The ebook is self contained and obtainable. The authors stick with a scientific trend for every bankruptcy together with a number of examples and routines 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 similar topics.

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

**Example text**

If inﬂation rates are between 3% and 5% during that time, then they need to save more than twice as much as the current estimate since increases in the cost of education typically outpace inﬂation. • We notice that Pn is directly proportional to P0 but is a nonlinear function of iinf and n. 10 on p. 52 ask you to prove these conjectures. • If iinf > 0, then {Pn } is a decreasing sequence for which limn→∞ Pn = 0. Thus, during times of inﬂation, our money buys less and less as time goes by. • If iinf < 0—this is usually called deflation—then {Pn } is an increasing sequence for which limn→∞ Pn = ∞.

2), we have 1 + ireal = 1 + ieﬀ . 1 + iinf This can be rewritten as ireal = 1 + ieﬀ ieﬀ − iinf −1= . 1 + iinf 1 + iinf Thus, we have the following theorem. 2. The Inﬂation Theorem. If the annual inﬂation rate is iinf , then the real rate of interest, ireal , that corresponds to an annual eﬀective rate of ieﬀ , is ireal = ieﬀ − iinf . 3) for ieﬀ gives ieﬀ = iinf + ireal + iinf ireal . 2 Consumer Price Index (CPI) The Consumer Price Index (CPI) is a measure of the average price over time of a ﬁxed market basket of goods and services bought by consumers for day-today living.

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.