9. Obtained at a bank, on my note payable in 6 mo., money enough to buy 20 acres of land at $100 per acre. The day my note at the bank became due, I sold the land for $2062.32 cash. Did I gain or lose by the transaction, and how much, money being worth 6 per cent per year?

10. Obtained at a bank, on my note payable in 4 months, money enough to buy 20 acres of land at $100 per acre. The day the note became due, I sold the land for cash, at such rate that the price of 18 acres was just sufficient to pay the note. How much did I gain by the transaction, money being worth 6 per cent?

11. Bought goods to the amount of $864.27 on a credit of 6 months; but the seller offering to deduct 5 per cent from the face of the bill if I would pay cash, I hired the requisite amount of money, giving my note payable in 6 months, with interest at 6 per cent per year, to be reckoned from date. For how much less than the value of the original bill could I pay the amount of this note?

12. I owed $800, due in 6 months; but my creditor offering to deduct 5 per cent of the debt for cash, I paid $380 down. How much did I still owe?

=

95

10%

=

Suggestion. - Since 5 per cent of the debt was to be deducted for cash, the cash payment would be 95 per cent, 18, of the part of debt it would cancel; or the part cancelled would be of the cash paid.

13. I owed $900, payable in 4 months; but my creditor offering to deduct 4 per cent of the debt for ready money, I paid $696 down. How much did I still owe?

198. To find the Rate.

Problems in which, the principal, interest, and time being given, we are required to find the rate, rarely occur in business life. The following solutions illustrate the principles which apply to them.

1. At what rate per cent must $648 be on interest to gain $81.873 in 2 yr. 3 mo. 17 da.?

Solution.

- The principal being equal to 648,000 mills, and the inter

81873

9097

est to 81,873 mills, the interest is = 648000 72000 of the principal. 2 yr. 3 mo. 17 da. =27 mo. 17 da. = 827 da. If the interest for 827

9097

9097

da.=2000 of the principal, the interest for 1 day must equal 827 of 72000 of the principal, and the interest for 1 yr., or 360 da., must equal 360 times the last result, or 327 of 72000

per cent.

Required the rate of interest when

=

200

=

.05252

2. $624 gains $74.88 in yr. 2 mo. 12 da.
3. $57.25 gains $5.038 in 1 yr. 5 mo. 18 da.
4. $855 gains $46.55 in 2 yr. 2 mo. 4 da.
5. $64.80 gains $6.246 in 11 mo. 17 da.

199. To find the Principal from the Interest.

Problems in which, the interest, rate, and time being given, we are required to find the principal, are, like those in the last article, of rare occurrence.

1. What principal on interest at 6 per cent will gain $37.47 in 1 yr. 3 mo.

Solution. 15 mo. = 20%

=

?

- At 6 per cent per year, the interest of any principal for of the principal. If $37.47 is of the princiof the principal must equal of $37.47, and the principal must equal 40 times the last result, or of $37.47, which is $449.60.

pal,

2. What principal on interest at 8 per cent will gain $26.18 in 1 yr. 4 mo. 15 da. ?

16

Since 1 yr. 4 mo. 15 da.

= 16 mo. =

12 yr.=

Solution. of yr., the interest must equal 11 of 8 per cent, or 11 per cent of the principal. If $26.18 is 11 per cent of the principal, 1 per cent of the principal must be TT of $26.18, which is $2.38, and 100 per cent, or the principal, must equal 100 times the last result, which is $238.

3. At 6 per cent will gain $8.73 in 5 mo. ?

4. At 6 per cent will gain $4.77 in 1 yr. 5 mo. 20 da. ?

5. At 5 per cent will gain $4.27 in 2 yr. 6 mo. ?

6. At 7 per cent will gain $116.127 in 4 yr. 4 mo. 4 da.?

200. Compound Interest.

When interest is to be paid at regular intervals, or, if unpaid, is to be added to the principal, to form a new principal on which interest is to be computed, it is called COMPOUND INTEREST. The following example illustrates this:

1. What is the compound interest of $784 for 2 at 6 per cent, payable annually?

e+f: = g

yr.
8 mo.

= amount due at end of 1st year.
interest for 2d year.

amount due at end of 2d year.

35.236 = interest for 8 mo.

916.138 =

a= 784.

amount due at end of 2 yr. 8 mo. = principal.

ga=h=$132.138 = compound interest for 2 yr. 8 mo.

2. To what sum will $437 amount in 2 yr. 6 mo. at 4 per rent, payable semiannually?

i+;=k=$482.483 = amount due at end of 2 yr. 6 mo.

interest 5th 6 mo.

3. What is the compound interest of $938.63 for 4 yr. 6 mo. at 6 per cent, payable annually?

4. What is the compound interest of $573.32 for 2 yr. 3 mo. at 8 per cent, payable quarterly?

5. To what sum will $1000 amount in 3 yr. 2 mo. at 6 per cent, payable annually?

6. To what sum will $500 amount in 4 yr. 3 mo. at 5 per cent, payable semiannually?

201. Table for Compound Interest.

Table showing what part of any principal is equal to its amount at 3, 4, 5, 6, 7, and 8 per cent annual compound interest, for any number of years not exceeding 25.

Yrs. 3 per cent. 4 per cent. 5 per cent. 6 per cent. 7 per cent. 8 per cent.

3. 1.092727 1.124864 1.157625 1.191016 1.2250431.259712 4. 1.125509 1.169858 1.215506 1.262477 1.310796 1.360489 5. 1.159274 1.216653 1.276281 1.338225 1.402552 1.469328

6.1.194052 1.265319 1.340096 1.418519 1.500730 1.586874 7.1.229874 1.315932 1.407100 1.503630 1.605781 1.713824 8. 1.266770 1.368569 1.477455 1.593848 1.718186 1.850930 9. 1.304773 1.423312 1.551328 1.689479 1.838459 1.999005 10. 1.343916 1.480244 1.628894 1.790848 1.967151 2.158925

11. 1.384234 1.539454 1.710339 1.898298 2.104852 2.331639 12. 1.425761 1.601032 1.795856 2.012196 2.252191 2.518170 13. 1.468534 1.665073 1.885649 2.132928 2.409845 2.719624 14. 1.512590 1.731676 1.979931 2.260903 2.578534 2.937194 15. 1.557967 1.800943 2.078928 2.396558 2.759031; 3.172169

16. 1.604706 1.872981 2.182874 2.540351 2.952164 3.425943 17. 1.652848 1.947900 2.292018 2.692772 3.158815 3.700018 18. 1.702433 2.025816 2.406619 2.854339 3.379932 3.996019 19. 1.753506 2.106849 2.526950 3.025599 3.616527 4.315701 20. 1.806111 2.191123 2.653298 3.207135 3.869684 4.660957

21.1.860294 2.278768 2.785962 3.399563 4.140562 5.033834 22. 1.916103 2.369918 2.925260 3.603537 4.430402 5.436540 23.1.973586 2.464715 3.071524 3.819749 4.740530 5.871464 24. 2.032794 2.563304 3.225100 4.048934 5.072367 6.341181 25.12.093778 2.665836 3.386355 4.291870 5.427433 6.848475

USE OF THE TABLE.

The amount of any sum of money,

at compound annual interest, for any time and rate mentioned in the table, may be found by multiplying the principal by the appropriate number selected from the table. This will be illustrated in the following examples and solution.

1. What is the amount of $245.73 for 12 yr. 6 mo. 20 da. annual compound interest at 6 per cent?

Solution. By the table, it appears that the amount of a sum for 12 years, at 6 per cent, compound interest, is 2.012196 times the principal. Multiplying $245.73 by 2.012196, we have $494.45692308, or, omitting the denominations below mills,

3 of a =

a= $494.457 = amount for 12 years.

b

= 16.481 interest for 6 mo. 20 da.

a+b=c=$510.938 amount for 12 yr. 6 mo. 20 da.

What is the amount at annual compound interest of
2. $578.67 for 11 yr. 4 mo. at 3 per cent?
3. $147.43 for 22 yr. 4 mo. 24 da. at 5 per cent?
4. $1467 for 18 yr. at 7 per cent?

What is the compound interest of

5. $1137.38 for 13 yr. 6 mo. at 6 per cent?
6. $328.96 for 9 yr. 3 mo. at 4 per cent?

202. Commission.

Money received for services in buying and selling goods for others is called COMMISSION, and is usually reckoned at a certain per cent of the cost of the goods bought, or price of those sold. A merchant who makes it his business to buy and sell on commission is called a COMMISSION MERCHANT. (See 177th page, Ex. 21, Note.)

1. A commission merchant sold goods for a manufacturer to the amount of $568.36, for which he charged a commission of 2 per cent. What was his commission, and how much will be due to the manufacturer ?