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240. Interest is compensation for the use of money.

241. The money for which interest is paid is called the principal.

242. The principal and interest together are called the amount.

NOTE.—Interest is usually reckoned in per cent, the principal being the base; that is, the borrower pays for the use of money a sum equal to a certain per cent of the principal. "The rate of interest” is the per cent per annum which the borrower agrees to pay.

When a man loans money "at 6%" he expects to receive back the principal, and a sum equal to 6% of the principal for every near the money is loaned and at that rate for fractions of years.

EXAMPLE.
Find the interest of $257 for two years at 6 %.

Explanation.

Operation. $2'57

.12 5.14 25.7

The interest of any sum for 2 years at 6 % is 12 hundredths of the principal. One hundredth of $257 is $2.57, and 12 hundredths of $257 is 12 times $257 or $30.84.

$30.84

1. Find the interest of $242 for 3 yr. at 7 %.
2. Find the interest of $375 for 2 yr. at 6 %.
3. Find the interest of $146 for 1 yr. at 5%.
4. Find the interest of $274 for 3 yr. at 5%.
5. Find the interest of $375 for 2 yr. at 8 %.
6. Find the interest of $864 for 3 yr. at 7 %.

(a) Find the sum of the six results.

Interest.

243. To COMPUTE INTEREST FOR ANY NUMBER OF YEARS

AND MONTHS.

NOTE.-The interest for 1 month is 1 twelfth as much as it is for 1 year; for 2 months, 2 twelfths or 1 sixth, etc.

EXAMPLE.
Find the interest of $324.50 for 2 yr. 5 mo. at 6%.

Operation and Explanation No. 1.
Interest of $324.50 for 1 year at 1%

$3.245
Interest of $324.50 for 1 year at 6% $19.470
Interest of $324.50 for 2 years at 6%

$38.940
Interest of $324.50 for 1 mo, at 6% $1.6225
Interest of $324.50 for 5 mo. at 6%

8.1125
Interest of $324.50 for 2 yr. 5 mo. at 6%

$47.0525 Operation No. 2.

E.rplanation. 2 yr. 5 mo. 212 years.

The interest of any sum for 2 yr. 21 times .06 = .143

5 mo. is 14] hundredths of the prin

cipal. $3'24.50

1 hundredth of $324.50 is $3.2450 .141

i hundredth of $324 50 is $1.6225 1.6225

4 hundredths of $324.50 is 12.9800

10 hundredths of $324.50 is 32.450 12.9800 32.450

141 hundredths of $324.50 is $47.0525 $47.0525

PROBLEMS. 1. Find the interest of $325.40 for 1 yr. 6 mo. at 7%.* 2. Find the interest of $420.38 for 2 yr. 10 mo. at 6%. 3. Find the interest of $221.60 for 2 yr. 3 mo. at 6%. 4. Find the interest of $145.20 for 1 yr. 9 mo. at 5%. 5. Find the interest of $340.10 for 3 yr. 1 mo. at 4%.

(a) Find the sum of the five results. * In an interest problem, if there is a fraction of a cent in the answer and this fraction is not greater than ], it may be disregarded; if it is more than ,, regaid it as 1 cent.

Interest.

244. To COMPUTE INTEREST FOR ANY NUMBER OF

YEARS, MONTHS AND DAYS.

Note.—In computing interest, 30 days is usually regarded as 1 month, and 360 days as 1 year; so each day is zo of a month or zło of a year.

EXAMPLE. Find the interest of $256.20 for 2 yr. 7 mo. 13 days at 6%.

OPERATION AND EXPLANATION No. 1.

Interest of $256.20 for 1 yr. at 1 %

$2.5620
Interest of $256.20 for 1 yr. at 6 % $15.3720
Interest of $256.20 for 2 yr. at 6 %

$30.7440
Interest of $256.20 for 1 mo. at 6 % $1.2810
Interest of $256.20 for 7 mo. at 6 %

$8.9670
Interest of $236.20 for 1 da. at 6 % $.04270
Interest of $256.20 for 13 da. at 6 %

.5551
Interest of $256.20 for 2 yr. 7 mo. 13 da. at 6 % = $40.2661

Operation No. 2.

E:cplanation. 2 yr. 7 mo, 13 da. 2; yr. 23 times .06 = .1543 The interest of any sum for 2 yr.

7 mo. 13 da. at 6 % is .1518 of the prin$2'56.20

cipal. .153%

1 hundredth of $256.20 is $2.5620 1.8361

23 of 1 hundredth of $256.20 is $1.8361

5 hundredths of $256.20 is $12.81 12.8100 25.620

$25.62 10 hundredths of $256.20 is

1588 hundredths of $256.20 is $40.2661 $40.2661

PROBLEMS.

1. Find the interest of $350.40 for 2 yr. 5 mo. 7 da. at 6 %. 2. Find the interest of $145.30 for 1 yr. 7 mo. 10 da. at 8 %. 3. Find the interest of $174.20 for 2 yr. 3 mo. 15 da. at 7%. 4. Find the interest of $253.40 for 3 yr. 6 mo. 20 da. at 5 %.

(a) Find the sum of the four results.

245. THE “ six-per-cent method." NOTE:-If the teacher so prefers, the problems on the three preceding pages, as well as those that follow, may be solved by the “six per cent method."

EXPLANATORY.
The interest at 6% for 1 yr. = .06 of the principal.
The interest at 6% for 1 mo. = ty of .06, or .005 of the principal.
The interest at 6% for 1 day zo of .005 or .000% of the principal.

READING EXERCISE. 1. Interest for 1 yr. at 6% 100ths of the principal;

=

for 2yr.
for 1mo.
for 3mo.
for 5ino.
for 1 da.
for 6 da.
for 18 da.
for 25 da.

100ths; for 3 yr.
-1000ths; for 2 mo =
-1000ths; for 4 mo. =
-1000ths; for 6 mo.
-1000th; for 3 da.
1000th; for 12 da.
1000ths; for 24 da.=
1000ths; for 27 da.=

-100tlis; -1000ths; 1000ths; -1000ths; -1000th;

1000ths; 1000ths; -1000ths;

Find the interest of $243.25 for 2 yr. 5 mo. 18 da. at 6%.

OPERATION AND EXPLANATION.

Interest for 2 yr.
Interest for 5 mo.=
Interest for 18 da.

Total interest =

.12 of the principal.
.025 of the principal.
.003 of the principal.
.148 of the principal.

$243.25 X .148 = $36 001*

*Nota Bene.

(1) $36.001 plus of $36 001 int. of same prin. for the same time at 7%.

(2) $36.001 less & of $36.001 = int. of same prin, for the same time at 5%.

(3) How find the interest at 8% ? at 9% ? at 4% ? at 3% ?

Interest.

246. PROBLEMS TO BE SOLVED BY THE “Six PER CENT

METHOD." 1. Find the interest of $265 for 1 yr. 3 mo. 13 da. at 6 %.* 2. Find the interest of $346 for 2 yr. 5 mo. 20 da. at 6 %. 3. Find the interest of $337 for 1 yr. 7 mo. 10 da. at 6%. I 4. Find the interest of $428 for 3 yr. 3 mo. 14 da. at 6%. 5. Find the interest of $150 for 1 yr. 6 mo. 15 da. at 6 %.

(a) Find the sum of the five results. 6. Find the interest of $245.30 for 6 mo. 18 da. at 7%. $ 7. Find the interest of $136.25 for 8 mo. 10 da. at 7 %. 8. Find the interest of $321.42 for 5 mo. 15 da. at 7 %. 9. Find the interest of $108.00 for 10 mo. 8 da, at 7 %. 10. Find the interest of $210.80 for 7 mo. 21 da. at 7%.

(b) Find the sum of the five results. 11. Find the amount of $56.25 for 2 yr. 4 mo. 2 da. at 6 %. 12. Find the amount of $31.48 for 1 yr. 5 mo. 11 da. at 6 %. 13. Find the amount of $55.36 for 2 yr. 8 mo. 12 da. at 6 %. 14. Find the amount of $82.75 for 2 yr. 10 mo. 8 da, at 6 %. 15. Find the amount of $27.35 for 1 yr. 1 mo. 1 da. at 6%.

(c) Find the sum of the five results. 16. Find the amount of $875 for 3 yr. 8 mo. 15 da. at 5%. 17. Find the amount of $346 for 2 yr. 6 mo. 12 da. at 4%. 18. Find the amount of $500 for 1 yr. 7 mo. 18 da. at 3%. 19. Find the amount of $600 for 2 yr. 5 mo. 21 da. at 8%. 20. Find the amount of $825 for 1 yr. 9 mo. 24 da. at 9 %.

(d) Find the sum of the five results.

* 1 yr.

3 mo.

.06 .015 .0023

† 2 yr.

5 mo. 20 da.

.12
.025
.0031

1 yr.
7 mo.

06. .035 .0013

13 da.

10 da.

.0963

Total .0771
Total .1483

Total & First find the interest at 6%; then add į of that sum to itself.

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