Download An Introduction to the Mathematics of Money: Saving and by David Lovelock, Marilou Mendel, A. Larry Wright PDF

By David Lovelock, Marilou Mendel, A. Larry Wright

This can be an undergraduate textbook at the easy elements of private discounts 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 easy genuine research instead of taking the latter as given. Proofs utilizing induction, recurrence kin and proofs by way of contradiction are coated. Inequalities similar to the Arithmetic-Geometric suggest Inequality and the Cauchy-Schwarz Inequality are used. uncomplicated issues in likelihood and records are awarded. the coed is brought to components of saving and making an investment which are of life-long functional use. those contain mark downs and checking money owed, certificate of deposit, scholar loans, charge cards, mortgages, trading bonds, and purchasing and promoting stocks.

The ebook is self contained and obtainable. The authors persist with a scientific development for every bankruptcy together with a number of examples and workouts making sure that the scholar offers with realities, instead of theoretical idealizations. it really is compatible for classes in arithmetic, making an investment, banking, monetary engineering, and comparable subject matters.

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

Example text

If the inflation rate iinf is a constant, then after n years, the purchasing power of our money is Pn = P0 (1 + ieff )n 1 1 + iinf n = P0 1 + ieff 1 + iinf n . 2) If iinf > ieff , then {Pn } is a decreasing sequence for which limn→∞ Pn = 0. 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 = ∞.

We use Fig. 7 to represent this general case. C0 C1 C2 0 1 2 Cn−1 Cn n−1 n ··· Fig. 7. Time diagram for general cash flows The net present value, NPV, of an investment is the difference between the present value of the cash inflows and the present value of the cash outflows, that is, NPV = C0 + C1 (1 + i)−1 + C2 (1 + i)−2 + · · · + Cn (1 + i)−n , where i is the prevailing interest rate. ) This interest rate is a function of the risk of the investment. When attempting to choose between two investments with the same risks, the investor generally chooses the one with the higher net present value.

60 1 0 2 $1,000 $2,000 Fig. 9. 9 shows how to decompose Fig. 8. 03725 per year. However, there are two things wrong with this. 0745 by 2 we have computed a simple interest rate. Second, we have not taken into account that the $2,000 and the $1,000 are deposited at different times. 0366. 0366. ) However, this technique does not take into account the second problem, namely, that the $2,000 was deposited at a different time from the $1,000. 60 to $1,000 plus the discounted value of $2,000, namely 2000(1 + r)−1 .

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