Cash and Basic Math

'Cash' - a term that is used in so many parts of life.  This very simple term can have a number of different definitions, depending on the need and the use.  Let's look at the term in some different circumstances and review the definition.



When you go into the convenience store, your friend asks, "You have any cash?", you know what he means.  He is using the term 'Cash' to refer to the various forms of currency that are used for retail transactions in the countries of the world.  In the United States, the currency is referred to in dollars and cents with 100 cents in each dollar.  The Unites States currency is made up of bills and coins.

Normally, most 'coins' are expressed in dollars using a decimal point to express the cents.  Standard denominations are the penny ($0.01), nickel ($0.05), dime ($0.10), and quarter ($0.25).  Other coins are also available, however not widely used, the half dollar ($0.50), one dollar ($1.00) and the two dollar ($2.00).

The 'bills' are paper money and these bills are available in the denominations of one dollar ($1.00), five dollar ($5.00), ten dollar ($10.00), twenty dollar ($20.00), fifty dollar ($50.00), and one hundred dollar ($100.00).  While other denominations are available, they are no longer in general circulation.

Each country in the world has some word which is used to describe their national currency.  Many countries may accept U.S. dollars for purchasing goods or services.  When you pay $19.75 in U.S. dollars for an item in another country, how do you know if this is the right amount based on the item's price?  This is exactly the problem that the banks in the world have experienced in the past, "How much of one country's currency can be fairly traded for the currency of another country?"  The financial institutions of the world resolved the problem by developing an exchange rate for each country's currency into the currency of the other countries.  Each country makes this information available to the citizens of the country.  In the United States, the exchange rates are normally printed in the financial section of major newspapers or available on the Internet.  These exchange rates are printed from the perspective of the country where the newspaper is printed, which means that exchange rates for other countries are printed as they relate to the dollar when the newspaper is printed in the United States.

If 'Cash' currency can express prices and transfer value, why isn't it used for everything?  'Cash' currency is known as a negotiable instrument.  This means that the ownership of the 'cash' is established by possession.  'Cash', if lost, can seldom be recovered.  'Cash' currency is bulky when dealing with large amounts and is subject to theft or robbery.  While 'bills' have a serial number, recording the serial numbers can be cumbersome.  Also, 'Cash' currency is the favorite method of completing illegal transactions.  Because of this, large amounts of cash cannot be used to pay for things.  All banks and retail establishments are required to report any transaction involving more than $5,000 cash.  While 'Cash' currency has its purpose and need, there are other options for handling 'Cash'.



In a television commercial, the announcer indicates that if cash is paid for the new car, then he will provide a rebate of $1,000.  This form of the word 'Cash' refers to a value which can be passed to the new car buyer through the use of a financial institution.  In order to handle large amounts of cash and eliminate the need for everyone to bury their 'cash' in the backyard, financial institutions were developed.  Please note that the terminology is 'financial institutions' instead of the common term of 'Bank'. While banks are the most prevalent form of financial institutions, it is not the only option available.  In the same general category as banks are savings and loan organizations and credit unions.  There are differences in the nature and structure of these organizations, which is why they are not all referred to as banks.

Make note: whenever the term 'financial institution' is used, there is an assumption that the financial institution is insured.  Banks, credit unions, and savings and loan organizations can be insured with the federal government.  This program was established after the depression of 1929 where a number of banks failed and the customers lost their money.  When considering a financial institution, make sure the institution is insured by the federal government.

Financial institutions allow customers to deposit cash and maintain a balance in the customer's account.  This balance can be dispersed as needed by the customer to other people or businesses through the bank or the relationships that the bank has with other banks.  Balances in a customer account are referred to as 'cleared funds', which means that the balance belongs solely to the customer and there are no outstanding claims against the customer balance.  These 'cleared funds' can be used to make payments where a cash payment is required or desired.  There are many ways in which a customer can access or disperse the funds in the customer account.



Businesses have long known that managing the incoming cash and outgoing cash is critical to the success of a business.  A 'Cash flow' report is designed to show this information to the business in a summary format.  Here's how it works.  When incoming cash is received, the business records the transaction as income.  When outgoing cash is spent, the business records those transactions as expenditures (expenses or assets).  The secret of success is making sure that the incoming cash is more than the outgoing cash.  The report starts at the top and shows all of the sources of incoming cash (normally sales for goods or services).  Next show all of the outgoing cash for expenditures by classification.  Then at the bottom, subtract the expenditures from the income and show the net amount.

Sounds like a bunch of work, doesn't it.  Well, if you have created a report for each preceding month, then you can see how this month compares to the results of the other months.  If the income is lower than normal, then you would investigate and make changes to get more income.  If any of the expenditure classification lines is more than other months, then you would find out why and make adjustments.  Are there any expenditure classifications lower than normal?  If so, is there a way to save money each month or was this a one time fluke?  This is one small part of managing a business but if the bottom is positive (more income than expenditures) then you are profitable.  If it is negative, then you need to figure out if there is anything you can do to make the income higher or the expenditures lower or it could lead to bankruptcy.

What most people don't realize is that this business report can also benefit people trying to manage personal finances.  As discussed earlier, sources of cash are income and outgoing cash are expenditures.  Knowing where money comes from (cash sources) and where it is spent (cash uses) allows you to be able to better control the cash flow to maximize your satisfaction.  If there is something you want to plan for, by looking at the expenditure classifications, you can determine if you are spending more than needed for a particular item.  Let's assume that the report shows that meals eaten out each month average $300 per month.  If you make more meals at home and eat out less often, you could save $100 - $150 per month and build up a lump sum for your something special.

Remember, since there is no way to pay for goods or services without cash, then sooner or later the cash sources must be more or equal to the cash uses.  Also, a business knows which sources generate cash and how the cash is used.  With this information, the business can plan on how much cash will be provided next month by the sources and how much cash will be required for the uses.  Being able to plan the incoming and outgoing of cash is essential to make sure there is always enough cash coming in to match what is spent (this is commonly referred to as 'budgeting').



Mastering basic math as it relates to cash is a skill that will serve you well all through your life.  The nice thing about math and cash is the simplicity.  There are no arcs or co-sine and no logarithms, no geometry and only very low level algebra.  If complex math is needed, then a computer spreadsheet program will work fine, but the simple math required for cash can be done in your head.

Everyone knows that two quarters make fifty cents, but what is the most efficient coin combination for $0.72? It is two quarters, two dimes and two pennies.  While there are other combinations possible, most people prefer to receive the least number of coins and bills possible.  When you need to get rid of some coins the store will take seven dimes and two pennies, but when the store gives you change, you don't want a handful of nickels and pennies.  Being able to calculate change is part of doing math skills in your head.

In the convenience store or fast food outlet, most cash registers take a series of items entered by a cashier, provide a total and then provide the amount of change due from the amount that was tendered (amount given by the customer).  Can you calculate the amount of change due in your head?  While cash register bar code scanning identifies the product and the proper price (in most cases), the amount tendered is normally entered by the cashier.  If they enter the wrong number, can you calculate how much change you should get?  Assume that the cashier entered $4.00 instead of $5.00 on a $1.64 purchase.  Would you notice the difference between $3.36 instead of $2.36?  Don't be surprised if cashiers can't do this in their heads as they rely on the results shown on the screen.

Basic math skills are developed and strengthened over time with use.  Can you keep a running total in your head while shopping?  Can you calculate basic percentage discounts when purchasing sale items to know if you are paying the right amount?  Can you calculate the tip when eating in a restaurant without pulling out a calculator?

Most of these things are easy to do and, with a little practice, will become a skill that will be used for the rest of your life.  Here are a few basic math shortcuts to help in the process.  These are just suggestions and you should use what works best for you.  First and foremost, the most important concept to understand is that 'close' counts.  Because someone else will calculate the total on a cash register, the goal is to know in advance a solid estimate.  All through school, you have been graded on getting the exact answer to problems, but in this case, 'close' counts so some shortcuts are okay.

Coins and Math: The currency in the United States is made up of coins and bills, and the right combination requires a little math.  Being able to choose the correct combination of coins to create the proper change is a process of addition and knowing in advance several of the basic combinations.  If the change due is 88 cents, then start with the combination of the largest possible group.  Three quarters are 75 cents, while four quarters are 100 cents, which is more than is needed so start with three quarters.  The next largest coin is a dime or 10 cents, when added to the previous 75 cents gives 85 cents (notice that another dime, or 10 cents, will be 95 cents which is more than needed).  Using the next coin, the nickel or 5 cents, will bring the total to more than needed, three pennies should be used to make 88 cents.  Always start with the largest coin possible and continue adding until the result is more than needed, then go to the next coin.  The proper combination can always be found which results in the least number of coins.

Calculate Change: Calculating change is often thought to be complicated because you have to deal with both dollars and cents.  Instead of doing one big problem, do two smaller problems.  Break the problem into the two parts, the dollars and the cents.  You are dealing with two amounts, the amount due and the amount tendered.  Here's an example: the amount due is $7.59 and the amount tendered is $10.00.  The amount due cents is 59 and the amount tendered cents is 00.  The amount due dollars is 7 and the amount tendered dollars is 10.  First, if the amount due cents is larger than the amount tendered cents then increase the amount tendered cents by 100 and subtract 1 from the amount tendered dollars.  This leaves us with amount tendered cents of 100 and amount tendered dollars of 9.  Second, subtract the amount due cents from the amount tendered cents (100 - 59 = 41) giving the cents result of 41.  Third, subtract the amount due dollars from the amount tendered dollars (9 - 7 = 2) giving the dollar result of 2.  Now add them together for $2.41.

In a second example, assume that the amount due is $7.21 and the amount tendered is $10.25.  The amount due cents is 21 and the amount tendered cents is 25.  The amount due dollars is 7 and the amount tendered dollars is 10.  In this case, the amount due cents is smaller than the amount tendered cents so do not change the cents or the dollars.  Next, subtract the amount due cents from the amount tendered cents (25 - 21 = 4) giving the cents result of 4.  Third, subtract the amount due dollars from the amount tendered dollars (10 - 7 = 3) giving the dollar result of 3.  Now add them together for $3.04.  Yes, this is an exact answer but this is your money in change so don't get short changed.

Of course the third option is to look at everything as one big number.  Go back to the first example of amount due of $7.59 and amount tendered of $10.00.  Think of everything as cents so you have an amount due of 759 cents and amount tendered of 1,000 cents.  Subtract and you get 241 cents which is converted to dollars and cents of $2.41.  Pick the method that works for you.  Practice makes perfect and the more you do this, even slowly, will become easier.

Running Total: No, this isn't a marathon but it is an exercise in short term memory.  A running total sounds difficult but can be rather easy if you remember that the goal is not to be exact but to be close.  Start by understanding the required level of accuracy.  If you are going to purchase 4 items and spend $50 then the level of accuracy drops.  You can round to the next nickel or dime or dollar, whichever works best.  The alternate example would be buying 30 items and wanting to keep the total to $50 (that's an average price of $1.67).  In this case, round up to the next dime.  An item that is marked $1.34 should be added in at $1.40.  Reducing the level of accuracy makes the calculation easier.  Adding numbers together is the same process as subtracting for change.  If you have a total of $9.80 and the next item is $2.40, then once again break the $2.40 into dollars and cents or $2 and 40 cents.  The previous total is $9 and 80 cents.  Add together the cents.  Is the total more than 100 cents?  If so, add 1 to the previous $9 and keep the remaining cents, or 80 cents plus 40 cents equals 120 cents or $1 and 20 cents, added to the previous $9 is $10 and 20 cents.  Now add the dollar amount of the item, in this case $2 to the new total resulting in $12 and 20 cents or $12.20.  Yes, keeping track of the subtotals is difficult but can be learned easily and, once learned, helps with other short term memory problems (like a shopping list).

Getting to the check out and finding you don't have enough money can be very embarrassing and can be avoided.  These little tricks not only help to avoid embarrassing situations, but also provide mental exercises and the more these basic skills are used, the easier they become.

Basic Multiplication and Division: Basic multiplication and division skills are needed to calculate tips and discounts for sales.  Most of the time, these calculations are easy if you understand the shortcuts.

     1. Tips: Start with the example of tips calculated at 15%. Look at the total on the bill and move the decimal one space to the left or on a bill of $47.54 move the decimal so the result is $4.75. This result is 10% of the bill, now take 1/2 of the $4.75 or about $2.50 (remember, don't try to be exact) and then add the two numbers together: $4.75 and $2.50 equals $7.25 (most waiters and waitresses don't mind if you round up.)  So, by adding the numbers together, you get an idea of how much tip to leave. How much would you leave if you want a 20% tip?

     2. Sales Discounts: Next, the calculation of a discount is the same as the tip but subtract the result from the original amount. The original price is $31.99, so round up to $32.00.  The discount is 20% off, so what is the adjusted price?  Move the decimal place one position to the left ($3.20) and multiply by two to get from 10% to 20% ($6.40), then subtracted from $32.00 making a net price of $25.60.

     3. Other Discounts to Fractions: Many discounts are 25% off or 33% off.  Many times, these discounts are easier to calculate by flipping the discount from a percentage to a fraction: 25% discount is 1/4 off and 33% discount is 1/3 off.  In these cases, divide the price by 4 (on a 25% discount) or by 3 (with a 33% discount).  Assuming a 25% discount, $32.00 divided by 4 equals $8.00, then subtracted from $32 equals $24 as the sales price.

     4. Other Discounts Reversed: In some cases, it is easier to reverse the discount and multiply to get the adjusted price.  If the discount is 40% and the price is $49.99 (round to $50.00), then reverse the discount (subtract the discount from 100, getting 60% as the adjusted price after the discount). Multiply the price times the reverse discount: $50.00 times 60% equals $30.00.

     5. What Works for You: Everyone has a style that works easiest for them; just remember that close counts.  There are simple ways to perform most calculations relating to cash and money.  It requires taking a little time to figure out the easiest way.  Most important is to practice the various methods so that you can choose the one that works for you.

I know that some of this might seem unnecessary, but it is your money and you don't want someone else cheating you because they made a mistake.  The better you understand the basics of handling money, the more you are prepared to understand the value of money.  The value of money is based on knowing that some expenditures will have a greater value for a greater period of time than other purchases. cUsing money to the greatest possible value will help insure that you get the most out of your money and your life.