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Since 6 is of 12, and 5 is of 30, there are just—

as many cents as months, and
as many mills as days.

Therefore, to find the interest at 6%,

Regard of the months as cents, of the days as mills, and multiply their sum by the principal.

PROCESS.

=

2 yr., 2 x .06 = .12 8 mo., of 8 12 da., of 12 = .002

.04

$.162

WRITTEN EXERCISES.

1. Find the interest of $500 for 2 yr. 8 mo. 12 da. at 6%.

The interest for 2 yr. is $.12. Regarding of the months as cents, the interest for 8 mo. is $.04.

500
$81.000, Ans.

Regarding of the days as mills, the interest for 12 da. is $.002.

The interest on $1 for 2 yr. 6 mo. 12 da. is $.162, and the interest on

$500 is 500 times $.162, which is $81.

Find the interest at 6%

2. Of $450 for 3 yr. 4 mo. 6 da. 3. Of $525 for 2 yr. 6 mo. 12 da. 4. Of $600 for 3 yr. 5 mo. 18 da.

5. Of $125 for 1 yr. 10 mo. 18 da.
6. Of $24.50 for 3 yr. 8 mo. 24 da.
7. Of $1000 for 3 mo. 15 da.

8. Of $280.75 for 5 yr. 21 da. 9. Of $2000 for 4 yr. 10 mo. 24 da. 10. Of $5020 for 5 yr. 5 mo. 6 da. 11. Of $600 for 3 yr. 7 mo. 8 da. 12. Of $50.60 for 48 da. 13. Of $300 for 63 da.

Find the amount at 6%-
14. Of $34.60 for 4
yr. 9 mo.
15. Of $342.65 for 8 mo. 10 da.
16. Of $975.82 for 2 yr. 5 mo. 16 da.
17. Of $516.81 for 4 yr. 7 mo. 18 da.
18. Of $2400 for 10 yr. 10 mo. 10 da.

Find the interest

19. Of $600 for 2 yr. 10 mo. 12 da. at 5%.

PROCESS.

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20. Of $650 for 2 yr. 10 mo. 12 da. at 5%. 21. Of $3020 for 4 yr. 2 mo. 6 da. at 7%. 22. Of $15.63 for 3 yr. 1 mo. 5 da. at 51%. 23. Of $2000 for 5 yr. 5 mo. 5 da. at 5%.

24. Of $1625 from June 12, 1890, to Aug. 15, 1892, at 6%. 25. Of $415 from Oct. 10, 1891, to May 15, 1894, at 7%. 26. Of $500 from Apr. 14, 1890, to June 10, 1895, at 51%.

173. Method by Aliquot Parts.

WRITTEN EXERCISES.

1. What is the interest of $1200 for 4 yr. 5 mo. 15 da. at 5%?

PROCESS.

$1200

.05

$66.00
4

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Int. for lyr.

=

Int. for 4 yr.

Int. for 4 mo.

Int. for 1 mo.

Int. for 15 da.

2. Of $1080 for 3 yr. 9 mo. at 5%. 3. Of $720 for 2 yr. 8 mo. at 5%.

4. Of $840 for 4 yr. 7 mo. at 6%.

5. Of $1600 for 2 yr. 6 mo. 15 da. at 7%. 6. Of $3600 for 3 yr. 10 mo. 18 da. at 8%. 7. Of $4200 for 2 yr. 5 mo. 25 da. at 41%. 8. Of $1800 for 1 yr. 1 mo. 11 da. at 6%. 9. Of $2100 for 6 yr. 6 mo. 6 da. at 6%. 10. Of $2400 for 2 yr. 2 mo. 12 da. at 5%.

174. Exact Interest.

Exact Interest is interest obtained by reckoning 365 days to the year.

Exact Interest is used by the United States government and by many business men.

Common interest and exact interest for any number of years are the same. They differ only in periods of time less than a year.

Find the interest of $100 for 1 yr. at 5%.

Common Interest.

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It is thus seen that if

the remainder will be exact interest.

Hence

$730

.12

$87.60 Int. for 2 yr.

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Exact Interest.

$5

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off from common interest will give exact interest.

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WRITTEN EXERCISES.

yr.

1. Find the exact interest of $730 for 2 at 6%.

of common interest be subtracted from itself,

PROCESS.

$730
..043

7

2190
2920
73)$31.390(.43
292

219
219

=

$31.39
.43

73

8 mo. 18 da.

30.96
87.60

$118.56, Ans.

Find the exact interest of

2. $850 for 10 mo. 24 da, at 6%.

3. $1260 for 2 yr. 8 mo. 18 da. at 4%.

4. $2400 for 3 yr. 9 mo. 15 da. at 7%.

5. $1560 from Mar. 1st to Nov. 25th at 8%.

We find the common interest of $730 for 2 yr. by multiplying by .12, which is $87.60; and for 8 mo. 18 da. by multiplying by .043, which is $31.39.

Since off from common interest gives exact interest, we deduct s from $31.39, leaving $30.96, the exact interest for 8 mo. 18 da.

Adding $87.60 and $30.96, the result is $118.56.

6. $3330 from Jan. 4, 1888, to May 7, 1890, at 5%.

7. $960 from Mar. 12, 1890, to Dec. 20, 1890, at 51%.

8. $4080 from Dec. 11, 1892, to May 29, 1896, at 7%.

PROBLEMS IN INTEREST.

CASE I.

175. Given the time, rate, and interest, to find the principal.

WRITTEN EXERCISES.

1. What principal will in 2 yr. 6 mo. 12 da. at 6% give $30.40 interest?

PROCESS.

=

2 yr., 2 × .06 .12 6 mo., of 6 = .03 12 da., of 12 = .002 Int. of $1 $.152

$30.40.152

=

=

$200, Ans.

We find the interest of $1 for 2 yr. 6 mo. 12 da. to be $.152.

If $1 gains $.152, to gain $30.40 it will require as many dollars as .152 is contained times in 30.40, which is $200.

RULE.

Divide the given interest by the interest of $1 for the given time and rate.

What principal at interest will gain—

2. $105.60 in 3 yr. 8 mo. at 6%? 3. $11.76 in 4 yr. 8 mo. at 6% ? 4. $385 in 5 yr. 10 mo. at 6% ? 5. $1496 in 7 yr. 4 mo. at 6% ?

6. $45.625 in 2 yr. 6 mo. at 5% ?
7. $97.20 in 2 yr. 8 mo. 12 da. at 5% ?
8. $113.96 in 3 yr. 4 mo. 21 da. at 7%?

What principal will amount to

9. $1710.58 in 28 da. at 6% ?

10. $249.256 in 4 yr. 6 mo. at 31% ?

11. $1752.84 in 5 yr. 10 mo. 15 da. at 6%?

12. $32.82 in 7 yr. 7 mo. 21 da. at 5% ?

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