Chapter 3:
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2
𝑏
𝑏
The coordinates of the vertex of 𝑓(𝑥) = 𝑎𝑥 + 𝑏𝑥 + 𝑐 are (− 2𝑎 , 𝑓(− 2𝑎 ))
Chapter 4 Exponential and Logarithmic Functions
𝑦
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The exponential form of 𝑦 = 𝑙𝑜𝑔𝑏𝑥 is 𝑏 = 𝑥
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The logarithmic form of 𝑏 = 𝑥 is 𝑦 = 𝑙𝑜𝑔𝑏𝑥
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Change of base formula 𝑙𝑜𝑔𝑏𝑥 = 𝑙𝑜𝑔𝑎𝑏
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Simple interest 𝐼 = 𝑃𝑟𝑡
Basic Properties of Logarithms
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𝑙𝑜𝑔𝑏𝑏 = 1
𝑦
𝑙𝑜𝑔 𝑥
𝑎
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𝑙𝑜𝑔𝑏1 = 0
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𝑙𝑜𝑔𝑏(𝑏 ) = 𝑥
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𝑏
𝑥
𝑙𝑜𝑔𝑏𝑥
=𝑥
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Chapter 5 Mathematics of Finance
5.1 Compound Interest
𝑛
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Compound Interest Formula: 𝑆 = 𝑃(1 + 𝑟)
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The Effective rate 𝑟𝑒 that is equivalent to a nominal rate of r compounded n times a year is given by
𝑟 𝑛
𝑟𝑒 = (1 + 𝑛 ) − 1
5.2 Present Value
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Present Value: The principal P that must be invested at the periodic rate of r for n interest periods so that the compound amount is S is given by …. And is called the Present value of S.
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−𝑛
𝑃 = 𝑆(1 + 𝑟)
5.3 Interest Compounded Continuously
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Compound Amount under Continuous Interest: The compound amount S of a principal of P dollars after t years at an annual interest rate r compounded continuously
𝑟𝑡
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𝑆 = 𝑃𝑒
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Effective Rate under Continuous Interest: The effective rate corresponding to an annual rate of r compounded continuously is
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Present Value under Continuous Interest: The present value P of S dollars due at the end of t years at an annual rate of r compounded continuously
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𝑟
𝑟𝑒 = 𝑒 − 1
−𝑛
𝑃 = 𝑆𝑒
Equation of Values; An equation of value illustrates that when one is considering two methods of paying a debt at a time. The value of all payments under one method=the value of all payments under the
other method
0
