Exponential growth and interest
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The document discusses exponential growth and decay functions of the form y = a*rt, where a is the original amount, r is the rate, and t is time. It provides examples of rates for growth/decay, doubling, and half-life decay. It also shows how to convert between percentages and decimals and calculates compound interest and doubling time for investments growing at different rates.
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CHAPTER 5INTRODUCTION TO VALUATION THE TIME VALUE OF MONEY (C
CHAPTER 5
INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY (CALCULATOR)
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
4.1
This version relies primarily on the financial calculator with a brief presentation of formulas. The calculator discussed is the TI BA-II+. The slides are easy to modify for whatever calculator you prefer.
Determine the future value of an investment made today
Determine the present value of cash to be received at a future date
Find the return on an investment
Calculate how long it takes for an investment to reach a desired value
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Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
Future Value and Compounding
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Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
Present Value – earlier money on a time line
Future Value – later money on a time line
Interest rate – “exchange rate” between earlier money and later money
Discount rate
Cost of capital
Opportunity cost of capital
Required return
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Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
4.4
Section 5.1
It’s important to point out that there are many different ways to refer to the interest rate that we use in time value of money calculations. Students often get confused with the terminology, especially since they tend to think of an “interest rate” only in terms of loans and savings accounts.
Suppose you invest $1,000 for one year at 5% per year. What is the future value in one year?
Interest = 1,000(.05) = 50
Value in one year = principal + interest = 1,000 + 50 = 1,050
Future Value (FV) = 1,000(1 + .05) = 1,050
Suppose you leave the money in for another year. How much will you have two years from now?
FV = 1,000(1.05)(1.05) = 1,000(1.05)2 = 1,102.50
Future Value – Example 1
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
4.5
Section 5.1 (A)
Point out that we are just using algebra when deriving the FV formula. We have 1,000(1) + 1,000(.05) = 1,000(1+.05)
FV = PV(1 + r)t
FV = future value
PV = present value
r = period interest rate, expressed as a decimal
t = number of periods
Future value interest factor = (1 + r)t
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Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
Section 5.1 (A)
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CHAPTER 5INTRODUCTION TO VALUATION THE TIME VALUE OF MONEY (C
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Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
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Determine the future value of an investment made today
Determine the present value of cash to be received at a future date
Find the return on an investment
Calculate how long it takes for an investment to reach a desired value
Key Concepts and Skills
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
Future Value and Compounding
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Chapter Outline
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
Present Value – earlier money on a time line
Future Value – later money on a time line
Interest rate – “exchange rate” between earlier money and later money
Discount rate
Cost of capital
Opportunity cost of capital
Required return
Basic Definitions
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
4.4
Section 5.1
It’s important to point out that there are many different ways to refer to the interest rate that we use in time value of money calculations. Students often get confused with the terminology, especially since they tend to think of an “interest rate” only in terms of loans and savings accounts.
Suppose you invest $1,000 for one year at 5% per year. What is the future value in one year?
Interest = 1,000(.05) = 50
Value in one year = principal + interest = 1,000 + 50 = 1,050
Future Value (FV) = 1,000(1 + .05) = 1,050
Suppose you leave the money in for another year. How much will you have two years from now?
FV = 1,000(1.05)(1.05) = 1,000(1.05)2 = 1,102.50
Future Value – Example 1
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
5C-‹#›
4.5
Section 5.1 (A)
Point out that we are just using algebra when deriving the FV formula. We have 1,000(1) + 1,000(.05) = 1,000(1+.05)
FV = PV(1 + r)t
FV = future value
PV = present value
r = period interest rate, expressed as a decimal
t = number of periods
Future value interest factor = (1 + r)t
Future Value: General Formula
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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Section 5.1 (A)
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Rates
This slide set is a work in progress and is embedded in my Principles of Finance course, which is also a work in progress, that I teach to computer scientists and engineers
http://awesomefinance.weebly.com/
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Investment management performance is easily measured at any frequency and easily
compared to publicly traded benchmarks such as S&P500 and Barclays Agg indices. In
contrast, wealth management is concerned with custom portfolios evolving over multi-decade
horizons. Such long horizons make it impractical to assess the quality of employed strategies
ex-post, while singularly personalized nature of the objective - funding a set of goals specific to
each individual - makes it impossible to create a single observable benchmark similar to an
index. We suggest that indexing should be done not at the level of portfolios but strategies, in a
way reminiscent of target date funds, and evaluation should be done using Monte-Carlo
simulations. We propose a simple methodology for building personalized benchmarks based on
a combination of user starting financial state and arbitrary list of goals. Such benchmarks can
be used to realistically evaluate a client’s current financial situation and serve as a point of
departure for providing nuanced advice.
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Absolute value m3 breakout
This document contains 6 math word problems with multiple choice answers. Each problem involves solving a linear equation for its solution set. The problems cover finding the solution set of linear equations involving addition, subtraction, multiplication, and division of variables. The correct answers are sets of numbers including solutions such as {3,-11}, {-2,2}, and {10,-10}.
Kopec slideshare
Mi madre me pregunta a mí y a mi padre si podemos hacer la maleta. Prefiero aquella camiseta. Ayer yo almorcé a las dos de la tarde. Cuando era niña, cada noche a la hora de dormir, mi madre me cantaba.
Spanish Review
La madre le pregunta a su hijo y a su padre si pueden hacer la maleta. Eran las doce de la noche cuando Victoria llegó a casa. Prefiero esta camiseta. Ayer yo almorcé a las dos de la tarde. Cuando era niña, cada noche a la hora de dormir, mi madre me cantaba.
Brekaout ppt
The document contains a series of unrelated math problems involving trigonometric functions such as tangent, sine, and angles and sides of triangles. It provides multiple choice answers but no explanations connecting the problems or answers.
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The document contains a series of unrelated math problems involving trigonometric functions such as tangent, sine, and measurements of sides of triangles. It provides multiple choice answers but no explanations connecting the problems or answers.
5 proportions in triangles ncvps
This document discusses proportional relationships in triangles. It states that if a line is parallel to one side of a triangle and intersects the other two sides, it divides those sides proportionally. It also explains that if parallel lines intersect two crossing lines, the line segments formed are proportional. Finally, it notes that if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the other two sides of the triangle.
13 1 combinations and permutations ncvps
This document discusses combinations and permutations. It defines independent and dependent events, and explains that factorial (!) is used to calculate the arrangements and selections of objects. Permutations refer to arrangements where order matters, and are calculated using factorial. Combinations refer to selections where order does not matter, and are calculated using the combinations formula of n!/(n-r)!r!. The document provides examples of calculating 6!/3!, permutations of 5 kids lining up, and combinations of selecting 3 students from a class of 25.
Sine and cosine graphs ncvps
The document discusses sine and cosine graphs, noting that they are similar but sine passes through the origin at (0,0) while cosine passes through (0,1). It defines key properties of the graphs including amplitude, period, phase shift, and vertical shift. Amplitude refers to half the total height or distance from the middle. Period is the length of one complete cycle. Phase shift slides the graph left or right while vertical shift moves it up or down. An example equation, Y = sin(4x - 2) + 3, is provided to demonstrate how these properties are represented in the function.
exponent properties
1) When raising a number to the 0 power, the result is 1. Negative exponents can be made positive by moving them to the denominator.
2) To multiply powers of the same base, add the exponents. For example, 2x3 * 4x4 = 8x7.
3) To divide powers of the same base, subtract the exponents. For example, x5/x3 = x2.
11 1 exponent properties for ncvps
1) Anything to the zero power is 1. To make negative exponents positive, move them to the denominator.
2) Powers with the same base are multiplied by adding the exponents. Raising a power to a power is done by multiplying the exponents. Raising a product to a power distributes the power to each term.
3) To divide exponents, subtract the exponents and place the remaining base over the difference of the exponents.
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- 2. Exponential Function y = a • rt a = original amount, r = rate t= time Rate can be several things…. (1 ± %) for growth or decay (2) For “double” (1/2) for half life
- 3. 2) Change the following percent's to decimals: a) 23% b) 10% c) 5% d) 6.25%
- 4. 2) Change the following percent's to decimals: a) 23% b) 10% c) 5% d) 6.25% .23 .10 .05 .0625
- 5. Rates use “1” to represent staying the same, so • If something is growing by 3%, the rate is “1 + .03” or 1.03 • If something is shrinking by 5%, the rate is “1-.05” or .95
- 6. Continuously compounded interest A= Pe rt • Your bank is offering a savings account with a nominal rate of 1.5%,compounded continuously. If you deposit $1,000 in 2010, what will your balance be in 2020? P = principle (original amount) - $1000 R = rate - .015 T = time – 10 years Not a variable….use the NUMBER
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- 8. How long would it take a $500 investment to double if the interest was compounded continuously at 3%?
- 9. How long would it take a $500 investment to double if the interest was compounded continuously at 3%? 1000 = 500e .03t
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