413. Profits Computed as Interest. - In most business transactions when money is invested, the time of the investment is other than one year. Thus a man may buy and then sell in two months or'six months or a year and a half.

The rate of profit on a business investment is often computed as follows: All expenses are first deducted. This involves all outlays for work, rent, salaries of superintendents, etc. Then the investor sets aside a certain sum as compensation for his own work. What remains of the gain is regarded as interest on the money invested. This gives rise to problems like the following:

Example. A man invested $7800 in a business deal and closed it out in three months, making a gain of $940 over and above all expenses. What rate of interest did this investment yield?

Solution. Three months is of a year. Hence the gain for one year at this rate would be 4 X 940 Hence the rate of interest was 3760

= 3760.

divided by 7800

=

48.2%.

WRITTEN EXERCISES

In each of the following find the rate of interest to which the gain is

414. Quick and Slow Sales. An article which is sold quickly can be sold on a closer margin of profit than an article which must be kept in stock a long time. Hence there is a disadvantage in keeping a very large stock of goods on hand, that is, a large amount of each kind of goods, for in that case some of the goods are sure to be carried a long time. The disadvantage arises not only because of the item of interest on the money invested in the goods themselves, but also because of cost of insurance, the expenses of storage, etc.

In figuring the profit of a business, we consider the total investment of capital, and the net gain after all expenses have been paid.

PROBLEMS

1. A trader in farm implements has $60,000 invested in his busiHis net gain for one year is $8000. What is the rate of interest on this investment if the trader's own work is worth $3000 a year?

ness.

2. I bought a piece of land for $1500 and gave in payment a note dated September 5, 1916, with interest at 8%. May 20, 1918, I sold the land for $2500. After paying my note, what was my gain, assuming expenses of $400 and profits of $500 from rent?

3. Three men engage in business with $62,000 capital. The earnings for 4 months are $10,000, the expenses of conducting the business are $7500 including salaries. Find what rate of income was realized on the investment.

4. The income from a farm costing $23,000 was $4000, and the expenses were $2850. What was the gain per cent on the investment?

415. To Find the Time when Principal, Rate, and Interest are Given. Since Interest = Principal rate X time, it follows that the time can be found by dividing the interest by the product of the principal and the rate. But the product of the principal and the rate equals the interest for one year.

Hence we have the

Rule. To find the time divide the interest by the interest for one year. This problem is not of frequent occurrence.

416. To Find the Principal when Rate, Time, and Amount are Known.

Rule: Find the amount of $1 for the given time and rate and divide the given amount by it.

The reason for this rule will be apparent as soon as the statement of the rule itself is really comprehended.

Example. Find the principal if the amount in 5 mo. 18 da. at 5% is $1600.

The problem of this section is of comparatively frequent occurrence.

417. True Discount and Present Worth. In large transactions the method shown in the following examples is often used to decide how much an obligation due at a future time is worth at present.

Example 1. A note for $80,000 bearing no interest is due in 6 months. How much is it worth at present, the rate of interest being regarded as 6%?

Solution.

Amt. of $1 is 1.03

$80,000 ÷ 1.03 = $77,669.90 = present worth

Analysis: The problem is to find what principal must be invested at 6% to yield an amount of $80,000 in 6 mo. That is, it is the problem of § 416.

The principal which must be invested to amount to the value of a given sum at a given time is called the present worth of that sum, and the difference between this sum and its present worth is called true discount.

Example 2. Find the present worth and the true discount of a note for $1680 bearing interest at 7% and due in 80 days, the value of money being 51%.

$1706.13 1.01222 = $1685.53 = present worth and $1706.13-$1685.53= $20.60 is the true discount.

The rate of interest used in discounting the note is called the rate of discount. The rate of discount is frequently not the same as the rate of interest of the note.