Understanding the Mathematics of Personal Finance: An Introduction to Financial Literacy
Lawrence N. Dworsky
Format: PDF / Kindle (mobi) / ePub
A user-friendly presentation of the essential concepts and tools for calculating real costs and profits in personal finance
Understanding the Mathematics of Personal Finance explains how mathematics, a simple calculator, and basic computer spreadsheets can be used to break down and understand even the most complex loan structures. In an easy-to-follow style, the book clearly explains the workings of basic financial calculations, captures the concepts behind loans and interest in a step-by-step manner, and details how these steps can be implemented for practical purposes. Rather than simply providing investment and borrowing strategies, the author successfully equips readers with the skills needed to make accurate and effective decisions in all aspects of personal finance ventures, including mortgages, annuities, life insurance, and credit card debt.
The book begins with a primer on mathematics, covering the basics of arithmetic operations and notations, and proceeds to explore the concepts of interest, simple interest, and compound interest. Subsequent chapters illustrate the application of these concepts to common types of personal finance exchanges, including:
Loan amortization and savings
Mortgages, reverse mortgages, and viatical settlements
The book provides readers with the tools needed to calculate real costs and profits using various financial instruments. Mathematically inclined readers will enjoy the inclusion of mathematical derivations, but these sections are visually distinct from the text and can be skipped without the loss of content or complete understanding of the material. In addition, references to online calculators and instructions for building the calculations involved in a spreadsheet are provided. Furthermore, a related Web site features additional problem sets, the spreadsheet calculators that are referenced and used throughout the book, and links to various other financial calculators.
Understanding the Mathematics of Personal Finance is an excellent book for finance courses at the undergraduate level. It is also an essential reference for individuals who are interested in learning how to make effective financial decisions in their everyday lives.
the higher payments. 7. For the calculations in this problem, assume that the interest is compounded annually. Suppose you are able to take a 10-year loan at the loan rates shown in the table, and you are able to save the money for 10 years at the savings rates shown in the table. You borrow $10,000 and put it all into the savings account. Fill out the table. (This is known as working with “other people’s money.”) Loan rate (%) 5 5 5 6 6 7 10-year balance ($) Savings rate (%) 16,289 16,289
Example Start Month: Start Year: 7 2005 Nr Mnthly Pmts 360 Rate Monthly Pmt 4.50% $350.00 Pmt Nr Mnth Year Balance ($) 1 2 3 4 5 6 7 8 9 10 11 12 7 8 9 10 11 12 1 2 3 4 5 6 2005 2005 2005 2005 2005 2005 2006 2006 2006 2006 2006 2006 350.00 701.31 1,053.94 1,407.89 1,763.17 2,119.79 2,477.74 2,837.03 3,197.67 3,559.66 3,923.01 4,287.72 350.00 350.00 350.00 350.00 350.00 350.00 350.00 350.00 350.00 350.00 350.00 350.00 0.00 1.31 2.63 3.95 5.28 6.61 7.95 9.29 10.64 11.99 13.35 14.71
variables. The only difference is that the Principal variable on the Loan sheet has been replaced with a Monthly Pmt variable on the Save sheet. The variables to the right of the green line are the same on both spreadsheets. In the Savings sheet, however, the balance and the interest grow each month. I’ve 52 Chapter 3 Loan Amortization and Savings 300,000 Balance ($) 250,000 200,000 150,000 100,000 50,000 0 0 50 100 150 200 250 300 350 Deposit number (months) Figure 3.2 Example of
the full payment, everything gets zeroed out and my daily balances are 0 from the twelfth day until the end of the month. At the end of the month, the bank again calculates the ADB. This is a simple calculation—in each category, add up all the daily balances and then divide this number by the number of days in the month. Shown in the table are the purchase ADB of $123.77 and the cash advance ADB of $177.29. These ADBs in turn create interest payments of $1.12 and $3.35 for the purchase and cash
you’re feeding it “good” data—it will try to do its thing with whatever you type in. Ch13Stocks.xls is deceptively simple-looking—there are a lot of calculations going on behind the scene. The Correlation tab in Ch13Stocks.xls lets you look at two sets of stock prices and see how well they are or are not correlated. Table 13.1 shows a few examples of the use of this spreadsheet. These examples use a few data points—my purpose here is to show the use of the spreadsheet. Examples I and II are the