17. A business man has invested $5400 which yields 5% annually; $2000 which yields 4%; $1200 which yields 7%; and $800 which yields 81%. Find the rate of income on the total investment.

18. The value of the crops of the United States in a certain year was estimated to be $21,000,000,000. This was an increase of $8,500,000,000 over the value of the previous year. What was the per cent of increase?

19. Practice until you can write the sums on page 5, in the time indicated.

20. A square piece of cloth whose edge is 1 yd. shrinks until its edge is 35 in. By what per cent is the edge decreased? By what per cent is the area decreased?

21. One gram of fat produces 9 calories of heat; protein and carbohydrate produce each 4 calories per gram. Find the number of calories produced by a kilogram of beefsteak, a kilogram of bread, and a liter of milk. See problem 7, page 82. A liter of milk weighs 1032 grams.

22. An agricultural experiment station reports the following data from a farm in Indiana concerning the profits from poultry in the two successive years :

Find for each year, (a) the total income, (b) the average profit per hen, (c) the profit per hour on the labor, and (d) the rate per cent of increase of total profit the second year over. the first.

CHAPTER VI

INTEREST

48. Meaning of interest. Money paid for the use of money is called interest.

The amount of interest to be paid depends upon the amount of money borrowed and the length of time it is kept. It is usual to charge as interest an agreed upon per cent of the money borrowed for each year that it is kept. Henry wants to buy a plow to cost $50. He borrows the money from William Doyle and agrees to return the money at the end of one year and to pay 6% of the amount borrowed as interest for its use for the year. How much interest must he pay? How much money must he pay Mr. Doyle at the end of the year? If he borrows the money for two years, how much interest must he pay? If for 6 months?

The per cent to be paid each year is stated as a certain per cent per annum and this per cent is called the rate of interest. Per annum means for a year."

Exercise 51

1. A man borrows $500 and agrees to pay 5% interest each year. If he keeps it one year, how much interest does he owe? If two years? Three years? Six months?

2. Answer each of the preceding questions if the rate of interest were 8% instead of 5%; if it were 7%; if it were 4%; 3%.

3. Find the interest on $150 for 5 years at 3%; at 6%; at 9%.

4. Find the interest on $75 for 1 year at 8%; for 6 months at 8%.

5. What is the interest on $300 at 6% for 3 months?

6. Find the interest on $4560 for 5 years at 4%; for 6 years at 6%; 2 years at 5%.

7. If $375 is borrowed for 1 yr. 6 mo. at 8%, what sum must be paid at the end of that time?

Find the interest to the nearest cent on the following loans :

49. Expressing time as years. Since interest is computed at a certain rate for one year, it is necessary to be able to express any number of months and days as years.

Six months is what part of a year? What part of a year is 3 mo.? 4 mo.? 2 mo.? 5 mo.? 10 mo.? 7 mo.? 11 mo.?

In computing interest it is usual to consider 30 days a month and 12 months a year, and therefore 360 days a year. What part of a month is 3 days? 10 days? 5 days? 6 days? 12 days? 18 days? 23 days?

What part of a month is 15 days? What part of a year is 1 month? of a month?

What part of a year is 15 days? 10 days? 3 months 15 days?

Since we consider 360 days a year, what part of a year is 1 day? 3 days? 17 days? 50 days?

To express a number of years, months, and days as years, first express the months and days as days, divide this number of days by 360, and add this fraction to the number of years given.

1. 6 months; 3 months; 7 months.

2. 30 days; 15 days; 10 days; 3 days; 12 days.

3. 2 mo. 15 da. ; 1 mo. 10 da. ; 6 mo. 9 da. ; 7 mo. 2 da. 4. 1 yr. 15 da. ; 2 yr. 5 mo. ; 1 yr. 2 mo. 15 da.

5. 3 yr. 15 da. ; 5 yr. 7 mo. ; 2 yr.

1 mo.

8 da.

6. Find the interest on $1250 for 1 yr. 5 mo. 10 da. at 6%.

50. The interest formula. How is the interest found on a sum of money at a certain rate for one year? For a number of years?

If the sum of money is p dollars, the rate per annum r, and the number of years t, make a formula for finding the interest

i.

Remember that in this formula the time t must be expressed in years and that the rate r is the rate per annum. The formula i=prt should be remembered.

EXAMPLE. Find the interest on $2400 for 2 yr. 7 mo. 5 da. at 6%. SOLUTION.

2 yr.=720 da.

Use the formula in finding the interest on the given.