Speed Mathematics Simplified (65 page)

Move the decimal point two places to the right to convert the decimal to a percentage: 30%.

Suppose we want to know the percentage of mark-up in this same case? The net price is now our base, so the fraction is 7.80/18.20:

We see at once that the next digit of the answer will be 5 or more (2 into 10), so we can move the point over to convert to a percentage and round off to 40.7%.

Note how much more the mark-up is as a percentage than is the discount. This is always true, because the base (the net price) is smaller than the retail price.

Break-even

A common expression in many business endeavors is the phrase “break-even point.” There are many special applications, but in general the phrase describes the minimum quantity
(or volume) required before a product or operation can break even and begin to make a profit.

In tooling up for a new plastic toy, for instance, a manufacturer may have to spend $20,000 in research and die-making costs. If the toy sells for $1.00 retail and he gives the normal 50% plus 10% discount, then he receives 45¢ for each toy. His selling overhead may be 10%, his raw cost of plastic, manufacture, packing and shipping another 10%, and his general company overhead 20%, or a total of 40% of that 45¢ (since the manufacturer figures his volume on
his
sales volume, not the retail price). This leaves 60% of that 45¢ to pay back the cost of getting ready to produce the toy, or 27¢ each. How many toys does he have to sell before he begins to make a profit?

The answer is found by dividing the “contribution” of each sale (27¢) into the “plant account,” as it is often called:

He will have to sell roughly 74,000 of this toy before he recovers his initial investment. Once that investment has been recovered, however, he stands to make 27¢ profit for each toy sold.

A very similar type of calculation is used to determine the break-even point of volume for, say, a grocery store. In any break-even problem, certain assumptions are made about “fixed” costs, such as the plant account for the toy above, or the running expenses of a store, and “variable” costs, or costs that are incurred only when each sale is made.

If all the fixed costs for a certain store were $1,000 a month—including rent, salaries, insurance, etc.—and the average net profit before overhead was 12%, then it is not difficult to calculate how much volume this store must do in order to break even. 12% is the contribution of sales to fixed overhead,
or 12¢ on the dollar, so we divide the fixed cost again by the contribution:

This store must do over $8,300 a month in sales volume before it can meet its fixed costs. For every dollar above that it does each month, it returns 12¢ profit.

Commission

Salesmen, stockbrokerage houses, insurance agents, and many other companies and people are paid in commission rather than by salary.

Commission is a simple percentage of the gross, or retail price (or net price, depending on the agreement). If a real-estate broker arranges the sale of a house for $20,000 and earns a 5% commission, he gets $1,000.

Commissions vary widely. Salesmen, depending on the field of business, may earn from 1% or 2% to 15% or even more. Stockbrokers work on a sliding scale that goes down as the volume goes up, on the theory that there is about as much paper work in buying or selling $50 worth of stock as there is in buying or selling $100,000 worth. Advertising agencies traditionally get a 15% discount (commission) on the space they buy from magazines or newspapers and the time they buy on radio or television.

As in any percentage situation, you can start with any two known factors and calculate the third, unknown one.

These three cases represent each possible type of unknown. See if you can answer each of them:

A salesman is on 6% commission. He makes a $480 sale. How much commission does he earn by this sale?

Another salesman, on
8%
commission, earned $64 one afternoon. How much business did he write in order to get the commission of $64?

A third salesman, on orders totaling $1,300, earned $91 in commissions. What is his commission rate?

Cover the answers with your pad as you work these out.

The first salesman merely has to multiply $480 by .06. He earns $28.80.

The second salesman has to find the base. $64 is 8% of what? As you remember from the chapter on percentage, he determines the unknown base by dividing $64 by .08:

The third salesman also has to divide, but he divides his commission by the base in order to make sure of his rate. The answer is 7 %.

Interest

Most of us deal with interest in our personal lives, whether or not we deal very much with it in business. We buy homes almost invariably with a mortgage carrying interest charges. Often we buy automobiles, major appliances, furniture on “time payments” that include interest, whether or not the interest is called that. Sometimes it is called “carrying charges.” A bank loan or finance company loan always carries interest charges.

Compound interest is an intriguing subcategory that has little actual utility for most of us. It merely means that the interest is continually added to the principal on which interest is paid, so there is eventually a snowballing effect that can become quite dramatic after a century or two. Except for large interest rates and long periods of time, however, there is little difference in the results.

The interest you receive on your savings account, or the interest you pay on most mortgages, is a “real” interest, figured periodically on the amount of money the bank owes you or you owe the person holding the mortgage.

If you owe $16,000 on a 6% mortgage, the proper charge for one month for the use of this money is 1/12 of .06, or ½ of 1% (.005), which works out to $80. We use 1/12 of the
interest rate for one month because interest is (unless otherwise stated) figured by the year.

All fair and square. With your mastery of percentages, you should have no trouble with any problem in this area.

But interest, in today's world, has become quite a different thing for most of us. A lender may “prove” to you in black and white that he is charging you 8% interest, yet really can be quite legally gouging you to the extent of 16% or even more. This is so important to almost everybody who borrows money any time in his life that it is worth a page of special explanation.

Hidden Interest

Let us show how the most honest, time-honored, and respectable type of loan from the most inexpensive possible place works: a new-car loan from a bank.

Banks are by far the most reliable and safe places with which to do this kind of business. But when you take out a new-car loan and they say you will pay 6% interest, the reality is that you will pay more than 12%. At a finance company, this could easily go over 24% in real interest charges.

This is why:

When you borrow money and agree to pay interest for the use of it, you properly pay interest on the money while you have it. This is the way mortgages and savings accounts work. Each month (or quarter), the interest on the balance owed is figured and you pay it.

But it does not work this way with consumer loans.

Suppose you go to a bank to borrow, say, about $1,100 to help buy a new car. Your credit standing is good, so the bank says, “Fine.” They will charge you only 6% interest, deducted in advance. This means that you sign a note for $1,200, payable in 12 monthly installments. From this $1,200 they now deduct 6% interest for the year it will take you to pay back the loan. 6% of $1,200 is $72, so they give you a check for $1,128 and you buy your car.

The real interest on this loan is more than twice the 6% quoted. Why? For two reasons, First, you
never got
the $1,200
on which you pay the 6%. You got only $1,128. Second, you do not
have
the money for a year at all. You start paying it back the very next month—but the money you pay back the next month has had interest charged for a full year.

Here is how the interest would be charged if you were paying a real 6% on the amount you owe, making payments every month. We chose a $1,200 note to make the figuring easy, since you pay back $100 a month for a year.

The real
6%
interest on such a loan totals $34.68. The discounted-in-advance-for-the-full-term arrangement has you pay $72—over
twice
as much.

This illustration is not designed to malign banks. They are the most trustworthy of all such institutions. But if a quoted interest rate at a bank can be so deceptive, imagine what your real charges can become at finance companies when they talk about “only” 8% or 12% a year—discounted in advance.

BIBLIOGRAPHY

AMUSEMENTS IN MATHEMATICS

H. E. Dudeney; Dover Publications, N.Y.

ARITHMETICAL EXCURSIONS

Henry Bowers & Joan E. Bowers; Dover Publications, N.Y.

HIGH-SPEED MATH

Lester Meyers; D. Van Nostrand Company, Inc., N.Y.

HOW TO CALCULATE QUICKLY

Henry Sticker; Dover Publications, N.Y.

THE JAPANESE ABACUS: ITS USE AND THEORY

Takashi Kojima; Charles E. Tuttle Company, Rutland, Vt., and Tokyo

MAGIC WITH FIGURES