Write a computer program that implements all four formulas. Write your program in Python  since that is the computer program

Individual Homework Assignment

Economic Equivalence

Due date: Sunday, November 27, 2021 @ 11:59 PM

This assignment is an individual assignment and is based on the material covered in Chapter 8:

Economic Considerations and Models.

In Part 3 of the chapter, the primary focus was on the time value of money and the concept of

economic equivalence. For this assignment, you will use computer programming (reference

CSIT 512 Elements of Computer Programming) to implement an economic equivalence

program. Note: CSIT 512 was a prerequisite for IT 514 which is the prerequisite for IT 518.

The slides at the end of Part 3 presented the topic of economic equivalence and provided

example calculations using four variables defined as follows:

P = principle amount in $

F = future amount in $

i or r = interest rate

n = time in years

Given three of the four variables, the unknown value can be found using one of the following

formulas:

To find F: 𝐹 = 𝑃(1 + 𝑖)𝑛

To find P: 𝑃 = 𝐹

(1+𝑖)𝑛

To find n: 𝑛 = 𝑙𝑛⁡(

𝐹

𝑃 )

𝑙𝑛⁡(1+𝑖)

To find i: 𝑖 = ( 𝐹

𝑃 )

1

𝑛 − 1

Write a computer program that implements all four formulas. Write your program in Python

since that is the computer programming language taught in CSIT 512. You will need to import

the Math library for the program. If you wish to use a different language, you must obtain

approval from the professor prior to working on the assignment.

Program specifications:

1. The program must include comments. Comments should be included in the beginning of the

program to identify the programmer and provide a description of what the program does.

Comments should also precede each section of the program containing the formula calculations

that identify the calculation being coded.

2. You may define the known variables in the program or you may obtain them from user input.

There should be a definition of the values or input statements prior to the calculation. For

example, if you are calculating F, the values for i, P and n should immediately precede the

calculation. User input should also follow the same requirement.

3. Verify that each calculation is producing the correct result.

4. The output of each calculation must be printed with appropriate messages. The output should

include the input values and the calculated output.

For example:

The input values were: F = 5000, i = 5, n = 10

The value for P = 3069.56

5. Define appropriate variable names that relate to the value being represented.

Turn in a copy of your source code program and a copy of the output of your program.

Depending on the programming environment you use, the output may be a copy/paste or screen

shot of the content of the output.

Additional note:

For the formulas used to calculate the various unknown values, write the code that would use the

correct numeric value for percentages. The example provided above was to calculate the present

value (P) needed to generate a future amount of $5000 in 10 years at 5% interest. For this

example, whether you prompt the user for input or define the values in the code, the starting

values should be 5000, 10 and 5. Then in your code, you would convert the 5% to 0.05 for the

calculation. If you don’t do this, you will get the wrong answer. Do not assume the user will

know to enter the decimal equivalent of the percent value. If I ask a bank what the current

interest is on my savings account, they will tell me in %; e.g. 1%. They won’t say 0.01.

IT 518 Systems Engineering & Integration

Chapter 8: Economic Considerations and Models

Part 3

1 © Copyright 2020 Bill Pierce

Time Value of Money

• Limited resource – best use

• Project vs. project evaluations difficult

• Need “common denominator” • Money earns interest

• Today’s dollar worth more than future dollar

• Question is “how much more?”

2

Life Cycle Costs & Income Analysis

• Provides basis for project/alternative cost comparisons

• Interest Formulas • i = annual rate of interest (%) • n = number of interest yielding time periods (usually annual) • P = Principle amount (current dollar value) • A = Single amount in a series of n equal amounts at end of each interest

period

• F = Sum of compound amounts of A at interest rate i

3

Compounding – Single-Payment Compound-Amount

4

(1 + 𝑖)𝑛 Single-Payment Compound-Amount Factor

𝐹 = 𝑃(1 + 𝑖)𝑛 Eqivalence Formula

Summary of Interest Formulas

5

Geometric-Gradient-Series Formula

• Annual money flows increase or decrease over time by a constant percentage • g designates percentage change in magnitude of money flow from one period

to the next

• Magnitude of the tth flow is related to flow F1 defined as follows

6

𝐹𝑡 = 𝐹1(1 + 𝑔) 𝑡−1 𝑡 = 1,2, …,𝑛

Geometric-gradient series with g > 0

Economic Equivalence

• Economic Equivalence: two (or more) cost comparisons must have same • Sums of money

• Time frames

• Interest rates

• Wide range of formulas, tools, and techniques for evaluating economic equivalence • Ex: At an interest rate of 10% for 8 years, a principle amount of $1 is equivalent

to $2.144

• Appendix E: Interest Factor Tables

• Also calculated as (1 + 𝑟)𝑛= (1 + .1)8= 2.14358881 rounded to 2.144 • r = interest rate period

• n = number of time periods

7

Equivalence Function Diagrams (1)

• What value of i will make a principle amount of $1,500 equivalent to a final sum of $5K in 10 years (n=10)?

8

From the diagram, i is between 12% and 14%, from the slope of the curve, about 13%, the point of intersection.

Calculation: 𝑖 = ( 𝐹

𝑃 ) 1

𝑛 − 1

Equivalence Function Diagrams (2)

• What value of n will make a principal amount of $4,000 equivalent to a final sum of $8,000 if interest is 8%?

9

From the diagram, n is between 9 and 10 years.

Calculation: 𝑛 = ln(

𝐹

𝑃 )

ln(1+𝑖)