By David Lovelock

This is an undergraduate textbook at the uncomplicated elements 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 common genuine research instead of taking the latter as given. Proofs utilizing induction, recurrence family 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 statistics are awarded. the scholar is brought to parts of saving and making an investment which are of life-long functional use. those contain discount rates and checking bills, certificate of deposit, scholar loans, charge cards, mortgages, trading bonds, and purchasing and promoting stocks.

The ebook is self contained and available. The authors stick with a scientific development for every bankruptcy together with a number of examples and workouts making sure that the coed bargains 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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**Extra resources for An Introduction to the Mathematics of Money: Saving and Investing**

**Example text**

What is the IRR for this investment? 5. How long will it take for an investment of $1,000 to increase to $1,500 at a nominal interest rate of 7% compounded semi-annually? What is the IRR for this investment? 6. Tom lends a friend $1,000 on the condition that in 10 years, the friend repays $4,000. What is the IRR for this investment? 7. Wendy decides to save for her retirement starting on her 25th birthday. She puts $1,000 a year in an investment that earns 10% a year compounded annually. She does this for 20 years (she is then 45, and has invested $20,000) and then stops adding more money.

So the IRR is the rate that makes the present value of the expected future cash ﬂows equal to the initial cost of the investment. The IRR is useful for comparing investments with diﬀerent costs or with cash ﬂows that diﬀer in terms of amount or frequency of payment, and for determining how a potential investment compares with the investor’s requirements. 32 2 Compound Interest From 1 + i = (1 + iirr )1/m we ﬁnd that iirr = (1 + i)m − 1, which relates the internal rate of return, iirr , to the periodic internal rate of return, i.

9% compounded continuously. Which has the highest IRR? 25. Tom Kendrick is considering two investments with cash ﬂows Years Cash Flow 0 −$13,000 1 $5,000 2 $6,000 3 . $7,000 What is the IRR? Give an explanation of these cash ﬂows in terms of everyday experiences, starting with “If I borrow . 26. Show that P0 (1 + x)n is an increasing, concave up function of x. (See p. 27. Show that P0 (1 + i)x is an increasing, concave up function of x. (See p. 28. Show, by induction, that for n > 1 and i > 0, n n (1 + 2i) − 1 > 2 ((1 + i) − 1) .