An Introduction to the Mathematics of Money: Saving and by David Lovelock

By David Lovelock

This is an undergraduate textbook at the easy facets of private rate reductions and making an investment with a balanced mixture of mathematical rigor and financial instinct. It makes use of regimen monetary calculations because the motivation and foundation for instruments of simple genuine research instead of taking the latter as given. Proofs utilizing induction, recurrence family and proofs via contradiction are coated. Inequalities similar to the Arithmetic-Geometric suggest Inequality and the Cauchy-Schwarz Inequality are used. simple issues in likelihood and information are offered. the coed is brought to parts of saving and making an investment which are of life-long sensible use. those comprise mark downs and checking money owed, certificate of deposit, pupil loans, charge cards, mortgages, trading bonds, and purchasing and promoting stocks.

The publication is self contained and available. The authors stick with a scientific trend for every bankruptcy together with numerous examples and routines making sure that the scholar bargains with realities, instead of theoretical idealizations. it truly is appropriate for classes in arithmetic, making an investment, banking, monetary engineering, and similar topics.

Show description

Read Online or Download An Introduction to the Mathematics of Money: Saving and Investing PDF

Similar management science books

Cyber-Physical Systems: Driving force for innovation in mobility, health, energy and production

This day, approximately ninety eight percentage of microprocessors are already embedded in daily items and units, hooked up with the surface global via sensors and actuators. they're more and more networked with each other and on the web. The actual international and the digital global - or our on-line world - are merging; cyber-physical platforms are constructing.

Organization Theory: Modern, Symbolic, and Postmodern Perspectives

Energetic and obviously written, this finished and cutting edge paintings offers a multi-disciplinary and modern creation to association concept. providing an even-handed, balanced appreciation of alternative views, its technique is pluralist, reflecting the various nature of organizational idea as a box of analysis motivated by means of thinkers from quite a few disciplines.

The Digital Transformation Playbook: Rethink Your Business for the Digital Age

Reconsider your small business for the electronic age. each company all started sooner than the net now faces an identical problem: how one can remodel to compete in a electronic financial system? Globally famous electronic professional David L. Rogers argues that electronic transformation isn't approximately updating your know-how yet approximately upgrading your strategic considering.

Extra info for An Introduction to the Mathematics of Money: Saving and Investing

Example text

The first equation is obtained by discounting to the present value, the second by compounding to the future value at the end of the twelfth month. Notice we assume that 1 + iirr > 0. If in the second equation we let 1 + i = (1 + iirr )1/12 , so 1 + i > 0, then we find that 100(1 + i)12 + 100(1 + i)11 + 100(1 + i)10 + · · · + 100(1 + i) = 1500. 5) We rewrite the equation as 11 (1 + i) 7 10 + (1 + i) + · · · + 1 (1 + i) = 15, We discuss stock market indexes in Chap. 10. 30 2 Compound Interest and then use the geometric series8 1 + x + x2 + · · · + xn−1 = (xn − 1)/(x − 1), valid for x = 1 and n ≥ 1, with x = 1 + i and n = 12, to find that i satisfies 12 (1 + i) i −1 (1 + i) − 15 = 0.

We now derive the general formula for this process. We let P n Pn m i(m) i be be be be be be the the the the the the amount invested at the end of every period, total number of periods, future value of the annuity at the end of the nth period, number of periods per year, nominal rate (annual interest rate), expressed as a decimal, interest rate per interest period. 1. 10 The interest rate per period is i = i(m) /m. We want to find a formula for the future value Pn , and we do this by looking at n = 1, n = 2, and so on, hoping to see a pattern.

3/i(∞) . 3, and it applies only if interest is compounded continuously. However, investments are frequently compound annually, not continuously. So what rule of thumb applies in this case? The answer is, there is no simple rule of thumb like “dividing a particular number by the interest rate”. In this case n Pn = P0 (1 + i) , so we want to find the N for which PN = 2P0 , or N (1 + i) = 2. Solving for N gives N= ln 2 . 693 by the natural logarithm of (1 + i). Not exactly a handy rule of thumb! 1.

Download PDF sample

Rated 4.74 of 5 – based on 14 votes