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A comprehensive introduction to exponents and logarithms in the context of finance. It covers concepts such as present value, annuities, optimal holding time, and logarithmic derivative. Examples, formulas, and applications of these concepts in finance, as well as exercises for practice. It is intended for students studying finance or economics, and can be used as study notes, lecture notes, summaries, or exercises to prepare for exams.
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7/29/2020 B02005 – Chapter 0: Introduction
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Introduce the present value. Define the form of the annuities. Identify and explain the optimal holding time. Introduce the logarithmic derivative. 7/29/2020 B03013^ –^ Chapter^ 2: Exponents and Logarithms 2
Example: You have started your first job and decide to put $200 a month into an annuity. The annuity earns 7.2% interest per year, compounded monthly. How long (in months and years) will it take for the account to be worth $1,000,000? 7/29/2020 B03007^ –^ Chapter 2: Exponents and Logarithms 14
7/29/2020 B03007^ –^ Chapter 2: Exponents and Logarithms 15
3) Suppose you own a rare book whose value at time t years from now will be B(t) = 2 √𝑡^ dollars. Assuming a constant interest rate of 5%, when is the best time to sell the book and invest the proceeds 7/29/2020 B03007^ – and Logarithms^ Chapter 2: Exponents 21