CHAPTER XXV

SIMPLE INTEREST

383. Frequency of Problems in Interest.

Of all the applications

There are few people

of percentage, interest is the most general. who do not need to figure interest at some time in their lives. Next to the four fundamental operations the subject of interest is probably the most important to the business man."

384. Interest. A man borrows $100 and at the end of one year he is obliged to pay back $106. The extra $6 which he pays is called interest.

385. Reason for Paying Interest. The custom of paying interest on borrowed money is now universal, and one cannot borrow in a business way without doing so.

On reflection the reasons for paying interest are obvious. If money could be borrowed without interest a man in a city could borrow, say $1000, to pay for the grading and beautifying of the lot around his house, and for the period between the borrowing of the money and the repayment of the loan, he would enjoy the increased beauty of his home with no extra expense to himself. Again, a farmer might borrow money to pay for clearing land, and up to the time of repaying the loan the increased production from the land would be clear gain. Under such circumstances, everybody would want to borrow and nobody would want to lend.

386. Interest on Investments in General. -The element of interest is by no means confined to cases where money has been loaned at a given rate. Any one engaging in business calculates to make a profit which first of all shall pay a reasonable rate of interest on the money invested. Stocks and bonds are bought because they yield dividends, and for no other reason. Every business investment is made on the expectation of a return that may be regarded as interest.

387. Principal, Amount.

- The amount on which interest is paid

is called the principal. The principal plus the interest is called the

amount.

388. Rate of Interest.

A certain per cent of the amount borrowed

is paid each year as interest.

The rate per cent of the principal which is paid each year as interest is called the rate of interest.

389. Time. In computing interest time is an essential element. That is, the interest is figured as so many per cent for a certain unit of time. The unit of time used in specifying the rate of interest is nearly always one year.

Thus, when we say that the rate of interest is 6%, we mean that 6% of the principal is paid each year as interest.

390. Interest Compared with Percentage.

When the time is

one year, problems in interest are problems in ordinary percentage. The principal is the base.

The rate of interest is the rate per cent.

The interest is the percentage.

The amount is the same in both.

ORAL EXERCISES

Find the interest in each of the following, the time in each being

WRITTEN EXERCISES

Find the interest in each of the following, the time being one year.

391. Time Other Than One Year. In long time loans with simple interest, the interest is payable yearly and the time involved in each computation is therefore one year. Problems arise, however, in which the time is several years. In such cases, the interest is the interest for one year multiplied by the number of years.

Thus, the interest on $800 at 6% for four years is 4 times the interest for one year, or 4 X $48

=

$192.

392. Time Less Than One Year. A very large number of loans are made for less than one year, and such loans give rise to the more difficult problems in interest.

To find the interest for a fraction of a year, the interest for a whole year is multiplied by this fraction.

Thus, to find the interest on $500 at 6% for of a year, the interest for one year, or $30, is multiplied by, obtaining $10.

Similarly to find the interest on $500 at 6% for of a year, $30 is multiplied by, obtaining $7.50.

In the following exercises count one month as one twelfth of one

MISCELLANEOUS WORK

1. Find the amount due the owner of a piece of property that sells for $6000, when 3% is allowed for selling.

2. Find the commission on the sale of 200 dozen eggs at 45¢ a dozen, when 2% is allowed for selling.

3. Find the proceeds on 200 bbl. of apples at $3.25 a bbl. after deducting 2% for selling, $40 for freight, and $25 for carting.

4. What is the rate of income if an investment of $108.50 yields $6 per year? ($6 is how many per cent of $108.50?)

5. How much must I pay for a permanent source of income of $7 to yield me 6% on my investment? ($7 is 6% of what amount?) 6. A merchant bought shirts at $9 per dozen. At what price per piece must he sell to make a profit of 50%?

7. A retail dealer buys goods listed at $85 at discounts of 20%, 15%, and 10%. At what price must he sell the goods to gain 35% on the purchase price?

8. A retail dealer bought goods for $5840, giving a commission of 14% for buying. He paid $840 for freight and other expenses. For how much must he sell the goods to make a profit of 30%?

9. A certain retail dealer in furniture sold a bill of goods for $204.80. The marking price of the articles sold would make them amount to $296.50. What was the rate per cent of his reduction? If this sale netted the dealer a gain of 17%, what would have been his gain per cent if he had sold at the marking price?

10. A retail dealer wishes to mark his goods so that he may reduce the marking price by 15% to his customers and still make 25% on the sale. How many per cent above his purchase must he mark the goods?

11. One man sells goods at a profit of 35% of the buying price and another sells goods at a profit of 25% of the selling price. Which makes the greater profit? If each of these men sells goods bought for $1000, what is the difference in their profits?