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EXERCISES. 1. Find the interest of:

1. $560 for 3 yr.
2. $636 for 5 mo.
3. $700 for 60 da.
4. $236 for 1 yr. 10 mo. 18 da.
5. $35.60 for 4 yr. 9 mo. 24 da.
6. $2000 for 4 mo. 15 da.
7. $390.86 for 6 yr. 24 da.
8. $3000 for 5 yr. 11 mo. 25 da.
9. $6030 for 6 yr. 6 mo. 7 da.

10. $700 for 4 yr. 8 mo. 9 da. 2. Find the amount of:

1. $45.70 for 5 yr. 10 mo.
2. $443.76 for 9 mo. 12 da.
3. $1085.93 for 3 yr. 6 mo. 18 da.
4. $627.92 for 5 yr. 8 mo. 19 da.
5. $113.96 for 9 yr. 9 mo. 9 da.
6. $5090 for 10 yr. 10 mo. 10 da.

7. $3500 for 11 yr. 11 mo. 11 da. 3. Find the interest of $700 for 3 yr. 10 mo. 13 da., at 5%.

3 yr.

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Process.
=.18
10 mo. = .05
13 da. .0023
.2327 X 700 = 162.517, int. at 6%.

6) 162.517
27.086, int. at 1%.

5
$135.430, int. at 5%.

NOTE.—Observe how the six per cent. method is applicable when other rates are given.

4. Find the interest of:

1. $760 for 3 yr. 11 mo. 12 da., at 5%.
2. $4030 for 5 yr. 3 mo. 7 da., at 7%.
3. $26.74 for 4 yr. 2 mo. 6 da., at 51%.
4. $3000 for 6 yr. 6 mo. 6 da., at 42%.
5. $2736 from July 12, 1897, to Sept. 15, 1898, at

5%.
6. $526 from Nov. 10, 1898, to June 16, 1900, at

7%. 7. $600 from May 15, 1890, to July 11, 1898, at

61%.

EXACT INTEREST.

=

Exactness requires that in reckoning interest for less than one year 365 days should be considered one year, and not 360 days. Hence

Pr. XR. X exact No. of days
Exact Int.

365 NOTE 1.–To find the exact number of days between two dates reckon each year as 365 days, and give to each month the number of days assigned it in the calendar. To be more exact, 366 days should be reckoned for each leap year and 29 days to February of every leap year, but in the following problems leap years are not considered.

NOTE 2.-Since 5 days = ts of 365 days, common interest diminished by 1g of itself will give exact interest for any number of days less than 365. CAUTION.—This does not apply to interest reckoned for one or more entire years.

Find the exact interest of $840, at 6%, from Mar. 3, 1894, to Aug. 24, 1897.

MODEL SOLUTION. From Mar. 3, 1894, to Mar. 3, 1897 = 3 yrs. 365 da. X 3 = 1095 days

Mar. Apr. May June July Aug. From Mar. 3, 1897, to Aug. 24, 1897=28+30+31+30+31+27= 174 days

Exact No. of days 1269 days

168 Pr. X R.X Exact No. of days 840 x .06 X 1269 Exact Int.

=$175.23 365

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=

363

EXERCISES. 1. Find the exact interest of:

1. $960 from Feb. 5, 1898, to Dec. 26, 1898, at 6%. 2. $2370 from Apr. 10, 1887, to Aug. 15, 1890,

at 5%. 3. $3500 from Jan. 1, 1891, to Nov. 20, 1895,

at 7%. 4. $2670 from May 29, 1890, to Mar. 4, 1891,

at 6%.

5. $4440 from Feb. 5, 1898, to Dec. 25, 1898, at 5%. 2. Find the exact amount of:

1. $747.37 from March 22, 1896, to Aug. 5, 1896,

at 6%. 2. $837.46 from April 3, 1896, to Dec. 21, 1897,

at 9% 3. $1094.94 from Sept. 2, 1896, to Sept. 2, 1898, at

10%. 4. $231.03 from Sept. 1, 1897, to Feb. 28, 1899,

at 6% 5. $556.44 from Jan. 1, 1893, to April 21, 1900, at

71%.

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To Find the Principal, the Rate, and the Time.

FORMULÆ.

Since Interest = Pr. X R. X yr., obviously

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Again, since Pr. X R. X yr. + Pr. Amount, and since Pr. X R. X yr. + Pr. = Pr. X (R. X yr. + 1), we have, Pr. X (R. X yr. + 1) = Amount, and

4. Pr.

Amt.
R. X yr. + 1

MODEL SOLUTIONS.

1. What principal will in 3 yr. 8 mo. 12 da. yield $1117.48 interest at 5% ?

Process.

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2. What principal will in 4 yr. 7 mo. 6 da. amount to $859.52 at 4%?

Process. 48

Amt. 7 mo. = 7 =55.2 mo.=

Pr.

R. X yr. + 1 6 da.

0.2 mo. 859.52

$725.946. .04 X 4.6 +1

4 yr.

mo.

mo.

4.6 yr.

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Or,

$1.00 in the given time will amount to .01 X 4 X 4.6 + 1.00 $1.184. Since $1.00 amounts to $1.184, and since some number of dollars multiplied by 1.184 yields $859.52, that number must be $859.52 = 1.184, or $725.946.

3. At what rate per cent. will $4220 produce $503.235 interest in 2 yr. 7 mo. 24 da. ?

2 yr.

mo.

mo.

Process. 24

Int. 7 mo. = 7 31.8 mo. = 2.65 yr. R.

Pr. Xyr. 24 da.

0.8 mo. 503.235

503.235

= .045 = 41%. 4220 x 2.65 11183

4. In what time will the interest on $4220 at 41% amount to $503.235?

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1. Find the principal that will :

1. Produce $180 int. in 6 yr. at 4%. 2. Produce $126 int. in 6 yr, at 61%. 3. Produce $200 int. in 16 yr. 6 mo. at 5%. 4. Produce $823.30 int. in 1 yr. 11 mo. at 6%. 5. Produce $6 int. in 14 mo. at 5%. 6. Produce $25 int. in 144 da. at 4!%. 7. Produce $669.64 int. in 1 yr. 7 mo. 12 da. at 6%. 8. Produce $2624.65 int. in 2 yr. 6 mo. at 5%. 9. Produce $1680 in 6 yr. at 4%. 10. Produce $840 in 3 yr. at 41%. 11. Amount to $45,056.92 in 2 yr. 6 mo. at 5%. 12. Amount to $3000 in 42 da. at 51%. 13. Amount to $595.20 in 16 mo. at 6%. 14. Amount to $3189.375 in 2 yr. 2 mo. at 5%. 15. Amount to $10,523.475 in 1 yr. 11 mo. 21 da.

at 41%. 16. Amount to $360.18 in 4 yr. 6 mo. 18 da. at 5%. 17. Amount to $770.50 in 2 yr. 7 mo. 15 da. at 6%. 18. Amount to $47,187.58 in 3 yr. 8 mo. 25 da. at

41%. 19. Amount to $5133.30 in 4 yr. 6 mo. 27 da. at 6%.

20. Amount to $950 in 3 yr. 3 mo. 3 da. at 7%. 2. At what rate will :

1. $1800 gain $396 in 3 yr. 8 mo.?
2. $852 gain $106.50 in 2 yr. 6 mo.?

.
3. $660 gain $192.50 in 5 yr. 10 mo.?
4. $840 gain $107,80 in 2 yr. 4 mo.?

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