3. Answer the questions in exercise 1 concerning the note in exercise 2.

4. Copy and fill out the following table:

5. On June 1 Robert Connell buys a threshing machine from a dealer for $2400 and gives in payment three notes without interest. One note is for $1000 and is due in 6 months; one is for $600, due in 1 year; and the third is for $800 and is due in 18 months. The dealer sells these notes to a bank August 22. Find the proceeds, if discounted at 5%.

NOTE. When the discount period is more than one year count the number of years and the exact number of days in the remaining part of a year.

6. A man sells a house and lot for $3200. He takes in payment $1500 cash and a note for the balance due in one year and bearing 5% interest. He at once discounts the note at a bank at 6%. How much cash does he receive for his property?

7. A hardware dealer sells farming implements which cost him $3456 at a profit of 25%. He takes in payment notes due in 90 days without interest. He discounts $1200 of these notes at a bank the day they are given at 7%. He discounts $1500 of them 45 days after they are given at 7%. One note for $200 is paid in full when due. The remainder of the notes are not paid promptly and the dealer pays an attorney 5% for collecting them. What were the dealer's net profits on the whole transaction?

84. Compound interest. A principal is said to be drawing compound interest if at the end of each period when interest is due the interest is added to the principal and the interest for the next period is computed on this sum.

If the interest is added to the principal at the end of each year, the interest is said to be compounded annually; if the interest is added to the principal at the end of each six months, the interest is said to be compounded semi-annually; if at the end of each three months, the interest is said to be compounded quarterly.

EXAMPLE 1. Find the compound interest on $1000 at 5% for 2 years compounded annually.

1102.50 amount at end of the second year.
1000

$102.50 compound interest for two years.

EXAMPLE 2. John deposits $100 in a savings bank which pays 4% interest compounded semi-annually. How much is due him at the end of a year?

SOLUTION. $100

.02

2 interest for the first 6 months.

100

102 amount due at the end of the first 6 months. .02

2.04 interest for the second 6 months.

102

$104.04 amount due at the end of the year.

Find the interest compounded semi-annually on

7. $600 for 2 years at 3%.

8. $1800 for 1 yr. 6 mo. at 2%.

9. $648 for 3 years at 4%.

Find the interest, compounded quarterly, on

10. $900 for 1 year at 4%.

12. $235 for 1 year at 5%. 13. $600 for 6 mo. at 4%.

11. $80 for 9 months at 3%. 14. Find the interest compounded annually on $600 for 3 yr. 8 mo. 10 da. at 4%.

SOLUTION. The compound amount of $600 for 3 yr. at 4% $674.92.

The interest on $674.92 for 8 mo. 10 da. at 4% = $18.75.
$674.92+$18.75-$600 = $93.67, the compound interest.

Find the interest compounded annually on

15. $1000 for 2 yr. 6 mo. at 4%.

16. $3500 for 2 yr. 5 mo. 12 da. at 2%.

=

85. Compound interest by tables. The laws of most states prohibit the collection of compound interest on notes. But compound interest is of much importance in finding the amount due on deposits in savings banks, and in finding the returns on long-time investments such as are made by insurance companies, banks, and other corporations that expect to collect the interest when due and reinvest it. In such cases compound interest is computed by the use of tables.

A TABLE GIVING THE COMPOUND AMOUNT OF $1 FOR ANY NUMBER OF PERIODS UP TO 20.

PERIODS 1 PER CENT 1 PER CENT 2 PER CENT 2 PER CENT 3 PER CENT PERIODS

1234567α

9

10 11

123456789

1.010000 1.015000 1.020000 1.025000 1.030000 1.020100 1.030225 1.040400 1.050625 1.060900 1.030301 1.045678 1.061208 1.076891 1.092727 1.040604 1.061364 1.082432 1.103813 1.125509 1.051010 1.077284 1.104081 1.131408 1.159274 1.061520 1.093443 1.126162 1.159693 1.194052 1.072135 1.109845 1.148686 1.188686 1.229874 8 1.082857 1.126493 1.171660 1.218403 1.266770 1.093685 1.143390 | 1.195093 1.248863 1.304773 1.104622 1.160541 | 1.218994 1.280085 1.343916 10 1.115668 1.177949 1.243374 | 1.312087 1.384234 12 1.126825 1.195618 1.268242 1.344889 1.425761 13 1.138093 1.213552 1.293607 1.378511| 1.468534 14 1.149474 1.231756 1.319479 1.412974 1.512590 15 1.160969 1.250232 | 1.345868 1.448298 1.557967 1.172579 1.268985 1.372786 1.484506 1.604706 1.184304 1.288020 1.400241 1.521618 1.652847 18 1.196147 1.307341 1.428246 1.559659 1.702433 19 1.208109 1.326951| 1.456811 1.598650 1.753506 1.220190 1.346855 1.485947 1.638616 1.806111

16

17

20

11

12

13

14

15

16

17

18

19

20

PERIODS 3 PER CENT 4 PER CENT 44 PER CENT 5 PER CENT 6 PER CENT PERIODS

1234567

10

12345678

9

10

11

12

1.035000 1.040000 1.045000 1.050000 1.060000 1.071225 1.081600 1.092025 1.102500 1.123600 1.108718 1.124864 1.141166 1.157625 1.191016 1.147523 1.169859 1.192519 1.215506 1.262477 1.187686 1.216653 1.246182 1.2762821.338226 1.229255 1.265319 1.302260 1.340096 1.418519 1.272279 1.315932 1.360862 1.407100 1.503630 8 1.316809 1.368569 1.422100 1.477455 1.593848 9 1.362897 1.423312 1.486095 1.551328 1.689479 1.410598 1.480244 1.552969 1.628895 1.790848 11 1.459970 1.539454 1.622853 1.710339 1.898299 12 1.511069 1.601032 1.695881 1.795856 2.012197 13 1.563956 1.665074 1.772196 1.885649 2.132928 13 14 1.618695 1.731676 1.851945 1.979931 2.260904 14 15 1.675349 1.800944 1.935282 2.078928 2.396558 15 16 1.733986 1.872981 2.022370 2.182875 2.540352 16 17 1.794676 1.947901 2.113376 2.292018 2.692773 17 18 1.857489 2.025817 2.208478 2.406619 2.854339 18 19 1.922501 2.106849 2.307860 2.526950 3.025600 19 1.989789 2.191123 2.411714 2.653298 3.207136 20

EXAMPLE 1. Find the amount due and the compound interest on $600 for 10 years at 4%, compounded annually.

SOLUTION. From the table the compound amount of $1 for 10 years at 4% is $1.480244. Then the amount of $600 is 600 × $1.480244 = $888.15. Subtracting $600 from this amount leaves

$288.15, the compound interest.

EXAMPLE 2. Find the amount due and the compound interest on $560 for 3 years at 4%, compounded quarterly.

SOLUTION. Three years equal 12 quarters. One per cent interest is due at the end of each quarter. Hence the problem is the same as that of finding the compound interest for 12 years at 1%. From the table the compound amount of $1 for 12 years at 1% is $1.126825. 560×$1.126825=$631.02, the compound amount. The compound interest is $631.02-$560=$71.02.

Exercise 89

Use the table and find the compound interest on
1. $1200 for 6 years at 2%, compounded annually.
2. $859 for 10 years at 4%, compounded annually.

3. Find the interest in exercise 2, compounded semiannually. What is the difference in the two results?

4. $265.80 for 3 years at 4%, compounded quarterly.

5. $10 for 5 years at 6%, compounded quarterly.

6. $482 for 8 years at 3%, compounded semi-annually. 7. $1,000,000 for 10 years at 4%, compounded semiannually.

8. Mr. Tucker has a loan fund of $5000 which he lends at 6%. At the end of each year he lends all the interest which he has collected for the preceding year. What will the fund amount to at the end of 2 years? At the end of 3 years? Of 4 years?