LIMITATION OF LIABILITY/DISCLAIMER OF WARRANTY: THE PUBLISHER AND THE AUTHOR MAKE NO REPRESENTATIONS OR WARRANTIES REGARDING THE ACCURACY OR COMPLETENESS OF THE CONTENTS OF THIS WORK AND EXCLUDING IMPLIED WARRANTIES OF FITNESS FOR A PARTICULAR PURPOSE. And secondly to my husband, Ted, who is the family's financial guru and has had many years of experience in business and the financial arena.
Introduction
In other words, you'll find that the organization is set up so that you can quickly access the pages you need, when you need them. All the more power to you, but I think you'll still want to invest in a calculator.
Reviewing Basic Math for Business and Real Estate Transactionsand Real Estate Transactions
Similarly, computers and spreadsheet software are not a necessity, but I assume you can use a computer even if you don't have your own. I'll show you how to do these problems, but I'm assuming you've at least seen the algebraic process before and just need a reason to use it.
Taking Intriguing Math to Work
Discovering the Math of Finance and Investmentsof Finance and Investments
Putting Math to Use in Banking and Payrollin Banking and Payroll
Successfully Handling the Math Used in the World of Goods and ServicesUsed in the World of Goods and Services
Surviving the Math for Business Facilities and OperationsFacilities and Operations
The Part of Tens
If you need help with the basics, feel free to start with the first part. You just have to pick and choose what you need from the various parts of this book (and then use or abuse it to your heart's content).
Reviewing Basic Math for Business
So in this part you'll explore percentage increases and percentage decreases, and see how the math works out, along with fractions and ratios. You'll also discover how to create new ways to use percents and ratios that you haven't even thought of yet.
Starting from the Beginning
Starting from the Beginning
=axy Dealing with negative exponents Move the power to the denominator (a. the lower part of the fraction) and change the sign. To compare how much money accumulates, write a fraction with the 10 years in the numerator (the top part of the fraction) and the 5 years in the denominator (the bottom).
Fractions, Decimals, and Percents
Fractions, Decimals, and Percents
- Count the number of digits to be discarded, and think of the power of 10 that has as many zeros as digits to discard
- Use, as a comparison, half of that power of 10
- Now consider the discarded digits
You know that the sawdust makes up at least the last three decimal places of the number. You leave the 0 after the decimal point to indicate that the number is correct (rounded) to the nearest tenth.
Discovering irrational numbers
- Set the decimal equal to N
- Multiply both sides of the equation by the power of 10 that has as many zeros as there are nonrepeating digits
- Multiply both sides of the new equation by the power of 10 that has as many zeros as there are repeating digits
- Subtract the equation in Step 2 from the equation in Step 3, and solve for N
- Multiply both sides by 1,000 (because the 123 doesn’t repeat), which gives you 1,000N = 123.555555555
- Multiply each side of the equation in Step 2 by 10 (because only one digit, the 5, keeps repeating), and you get 10,000N =
- Subtract the equation in Step 2 from the equation in Step 3, and then solve for N
In this case, you round all digits to the right of the decimal point. A fraction is equivalent to another if the numerator and denominator are the same.
Determining Percent Increase and Decrease
Determining Percent Increase and Decrease
The percentage decrease is determined by multiplying the decimal equivalent of the percentage decrease by the original amount. To find the percentage reduction, you divide the amount of the reduction by the original value.
Dealing with Proportions and Basic Algebra
Dealing with Proportions and Basic Algebra
- Determine how many homes were sold from March 1 through April
- Solve for the number of homes sold by March 20
- Add the result from Step 2 to the 50 homes that were sold by March 1
Solve for x by cross multiplying and then dividing each side of the equation by the coefficient of x. Multiply both sides of the equation by the same number (but do not multiply by 0).
Taking Intriguing Math to Work
You can find formulas for measurements of physical structures and formulas for determining averages and other statistical values.
Working with Formulas
Working with Formulas
- Take roots and raise to powers
- Multiply and divide
- Add and subtract
Here's another example to help you practice unit conversion: What is the interest rate on a $21,000 loan at 9% annual interest if you borrow it for 90 days. An important part of this list of rules is the order of operations. The order of operations starts when you need to perform more than one operation in an expression. Try your hand at the order of operations with the example problems in the following sections.
Taking advantage of hand-held and online calculators
You must enter the numbers exactly in the correct order for the calculator to calculate what you mean. You can determine the monthly payment of a particular loan using one of the appropriate formulas (see Chapter 12 for more on loan formulas). The following is an option for the format of the formula (which is the one I use in my spreadsheet).
Reading Graphs and Charts
Reading Graphs and Charts
For example, if you want to create a line graph of the total city budget from 1993 to 2000, you might need to enter numbers in billions. On the left side of Figure 6-4 you see a graph of the total budget for 8 years. Create a histogram showing the number of hurricanes that hit the United States in each decade of the 20th century.
Measuring the World around You
Measuring the World around You
For example, to find the area of a rectangle, use a different formula than you would use to find the area of a triangle. If your region does not match any of the types shown in Figure 7-1, you must divide the region into rectangles or triangles and find the area of each. For example, to find the area of a triangular lawn whose sides measure 300, 400, and 500 yards, use Heron's formula.
Who was Heron of Alexandria?
The volume of any regular rectangular prism (more commonly known as a box) is obtained by multiplying the length by the width and height of the prism. Prism:V= Bh, where Bi is the area of the base and its height Pyramid:V 3 Bh. Now find the area of the triangular top of the room (which has a triangular base).
Heating and cooling the Great Pyramid
Do not confuse the base of the triangular prism used to find the volume of the three-dimensional figure with the base of the triangle used to find the area of the end piece of the room. Another beauty of the system is the way the different types of measures interact with each other. The scale in Figure 7-3 shows the relative positions of the various prefixes used in the metric system.
Blame it on the French: Discovering where the metric system came from
You just need to consider the actual size of the lumber you are buying if you need a particular thickness of wall or deck area. You can determine the total number of angle degrees within a polygon if you know how many sides it has. What is the total of the internal angle measurements of the area shown in the figure?
Analyzing Data and Statistics
Analyzing Data and Statistics
The mean average, 5,417, is not on the list of numbers, but it does somewhat describe the middle of the collection. Find both the mean age and the median age and decide which is a better representation of the average age. You know that the average of the list is 5, and you know that there are 23 numbers in the list.
Discovering the Math of Finance
Whether you're earning interest compounded quarterly or paying off an amortized loan, you're involved in the intricacies of interest, principal and percentages. With the chapters in this part, you can be better equipped to compare the many different financial products available. By the end of this, you will be ready to stand as your own financial advocate.
Computing Simple and Compound Interest
Computing Simple and Compound Interest
A simple interest formula allows you to save more than just the amount of accrued interest. The simple interest formula (which I explained earlier in the chapter) uses an annual interest rate and the number of years. First, to calculate ordinary interest, you divide the number of days by 360 (the number of days in a "normal" year), which gives you the fraction to use for the amount of time in the formula.
Don’t forget about the leap years!
6% or 90-day 4% rules
- Determine the value of the exponent by multiplying n × t (the number of times compounded each year times the number of years)
- Inside the parentheses, divide the interest rate, r, by the number of compoundings each year, n
- Add 1 to the answer in Step 2
- Raise the result from Step 3 to the power that you got in Step 1
- Multiply your answer from Step 4 by the principal, P
- Multiply 12 × 7 = 84
- Raise 1.00333 to the 84th power
Remember this: what you're really looking forward to is having a certain amount of money in the future if you're talking about current value. In other words, if you have a specific goal for a certain amount of money in the future, you want to know how much money you need to put down now (in the present) so that adding simple interest will create the sum of money you need. Calculating the total amount of money resulting from applying compound interest requires a jazzy formula.
The power of compound interest
- Simplify the fraction inside the parentheses
- Add 1 to the result of Step 1
- Raise the sum from Step 2 to the power outside the parentheses
- Subtract 1 from the number you get in Step 3
- Find the value of the exponent nt by multiplying the number of times you compound by the number of years
- Divide the rate, r, by n and add the result to 1
- Raise the sum (after adding the 1) to the nt power to get the value in the denominator of the fraction
- Divide the amount of money, A, by the denominator
The effective interest rate is what you get as a result of compounding that nominal rate. How much difference does using the effective interest rate (versus the nominal rate) make? It is clear that the increase in the interest rate after a year has the greater impact on the total amount.
Investing in the Future
Investing in the Future
What is the value of an investment of $100,000 after 2.5 years if it earns 12% annual interest compounded monthly. Some annuities are ordinary annuities and others are referred to as annuities paid. The main difference between the two types is when the payment is made. Consider this example for some practice: What is the present value of an ordinary annuity that earns 4% compounded quarterly if payments of $500 are made every 3 months (quarterly) for 10 years.
The easy way to sum up a series
In the earlier section, “Finding the Present Value of an Annuity,” you see how a lump sum can be equivalent to making regular payments. Using the formula for the present value of an ordinary annuity, you can solve for the number of payments, n. The deferred payment formula combines two other formulas: the present value of an ordinary annuity (to determine the amount of money needed at the start of the payout period) and the present value of that cash value (to determine how much you need) . to deposit now to have the required amount sometime in the future).
Understanding and Managing Investments
Understanding and Managing Investments
Counting on stocks with different indexes
To solve, let the price of the stock at the beginning of the year be represented by x. The stock dividend ratio is determined by dividing the dividend, $2, by the stock price, $98.04. You can determine the earnings per share of the stock if you have the price of the stock and the PE ratio.
Puts, calls, straddles, and spreads
The brokerage house sends you an invoice for 50% of the cost of the shares, which you pay. 7,700 the selling price of the share minus the cost of the share minus the interest payments. Nowadays any number of shares can be bought and the commission is a percentage of the purchase price.
Using Loans and Credit to Make Purchases
Using Loans and Credit to Make Purchases
But now you have inherited some money and want to pay off the rest of the loan. Then you realize that you are able to pay a little more than the monthly payment. You might think you're getting a good deal—until you do the math and determine that the total refund far exceeds the item's value.
Putting Math to Use in Banking
Managing Simple Bank Accounts
Managing Simple Bank Accounts
