2. Sold 24 yards of Holland, at 2 d. for the first yard, 4 d. for the second, 8 d. for the third, &c.; how much I did it amount to? Ans. 139810 L. 2 s. 6 d.

3. Bought 30 bushels of wheat, at 2 d. for the first bushel, 4 d. for the second, 8 d. for third, &c.; what does the whole amount to, and what is the price per bushel on an average?

Ans. {

8947848 L. 10 s. 6 d. Amount. 298261 L. 12 s. 4 d. per bushel. 4. A merchant sold 30 yards of lace, at 2 pins for the first yard, 6 for the second, 18 for the third, &c., and disposed of the pins at 1000 for a farthing; how much did he receive for the lace? and how much did he gain by the sale, supposing the lace cost him 100 L. per yd.? Received 214469929 L. 5 s. 3 d. Gained 214466929 L. 5 s. 3 d. 5. A goldsmith sold 1 lb. of gold, at a farthing for the first ounce, a penny for the second, 4 d. for the third, &c., in quadruple proportion; how much did he receive for the whole, and how much did he gain by the sale, supposing he gave 4 L. per ounce for the gold?

Ans.

Ans.

SHe received 5825 L. 8 s. 54 d. And gained 5777 L. 8 s. 54 d. 6. What sum would purchase a horse with 4 shoes, and eight nails in each shoe, at one farthing for the first nail, a halfpenny for the second, a penny for the third, &c. doubling to the last? Ans. 4473924 L. 5 s. 3 d.

7. A person married his daughter on new year's day, and gave her one dollar towards her portion, promising to double it on the first day of every month for one year; what was her portion? Ans. 4095 dois.

8. Suppose a man wrought 20 days, and received for the first day's labour 4 grains of corn, for the second 12, for the third 36, &c.; what did he receive for his labour, supposing 7680 grains to make a pint, and the whole to be sold at 2 s. 6 d. per bushel?

Ans. 1773 L. 7 s. 6 d.

0544

COMPOUND INTEREST,

BY DECIMALS.

The ratio in compound interest is the amount of one pound or dollar for one year; which is thus found:

As 1001: 105 : 1.05 As 100: :: 105.5: 1.055.

For quarterly amounts, take the 4th root of the ratio; for half yearly, the square root; and, for 3 quarters, the product of the quarterly and half yearly.

Thus, 1.03-1.007417; 1.03-1.014889; and 1.007417x1.014889-1.022416, for 3 quarters.

3

1.03 1.022416 1.014889 1.007417 .002500 31 1.035 1.026137 1.017349 1.008637 .002917 1.04 1.029852 1.019804 1.009853 .003333 1.045 1.033563 1.022252 1.011065 .003750 1.05 1.037270 1.024695 1.012272 .004167 1.055 1.040973 1.027132 1.013475 .004583 1.06 1.044671 1.029536 1.014674 .005000 61 1.065 1.048364 1.031988 1.015868 .005417

4

41

5

5

6

7

1.07 1.052053| 1.034408| 1.017058| .005833|

The ratio involved to the time is the amount of 1 L. or dollar for the time given; as a square for 2 years, a cube for 3, &c. thus, 1.06×1.06×1.06×1.06.

or 1.06-1.262477-the 4th power of 1.06, or the ratio involved to 4 years.

When the ratio is to be involved to years and quarters, the power for the years is to be multiplied by the proper quarterly amount; as, 1.262477×1.044671= 1.318873 for 44 years, &c.

The power or the amount of 1 L. or dollar may also be obtained for months and days (nearly) by adding the monthly simple interest of 1L. or dollar, or proper parts thereof, to the amount of the quarter next preceding the expiration of the given time, for what that time exceeds the said quarter; thus,

Amount for yr.

Int. of 1 L. for 1 mo.

1.029563: For 4 yrs.-1.318873 .005000 .005000

One sixth for 5 dys.= .000833

.000833

For 7 mo. 5 dys. 1.035396; For 4 years, 10 mo. 5 dys. 1.324706

The ratio may be thus involved to any time whatever; but the operation is facilitated by the following tables; which may be extended to 100 years, or upwards, by multiplying the amount for 46, by that for the time above 46, &c.

TABLE II. Showing the amount of 1 L. or Dollar from 1 year to 46.

Y.3 per cent.] 4 per cent. 44 per cent. 5 per cent. 5 per cent. 6 per cent. 11.0350000 1.0400000 1.0450000 1.0500000 1.0550000 1.0600000 1.0712250 1.0816000 1.0920250 1.1025000 1.1130250 1.1360000 81.1087178 1.1248640 1.1411661 1.1576250 1.1742413 1.1910160 41.1475230 1.1698585 1.1925186 1.2155062 1.2388246 1.2624769 51.1876863 1.2166529 1.2461819 1.2762815 1.3069598 1.3382256 61.2292553 1.2653190 1.3022601 1.3400956 1.3788426 1.4185191 71.2722792 1.3159317 1.3608618 1.4071004 1.4546789 1.5036302 81.3168090 1.3685690 1.4221006 1.4774554 1.5346862 1.5938480 91.3628973 1.42331181.4860951 1.5513282 1.6190939 1.6894789 101.4105987 1.4802442 1.5529694 1.6238946 1.7081440 1.7908476 111,4599697 1.5394540 1.6228530 1.7103393 1.8020919 1.8982985 121.5110686 1.6010322 1.6958814 1.7958563 1.9012069 2.0121964 131.5630560 1.6650735 1.7721961 1.8856491 2.0057732 2.1329282 141.6186945 1.7316764 1.8519449 1.9799316 2.1160907 2.2609039 151.6753488 1.8009435 1.9352824 2.0789281 2.2324756 2.3965581 161.7339860 1.8729812 2.0223701 2.1828745 2.3552617 2.5403517 171.7946755 1.94790052.1133768 2.2920183 2.4848011 2.6927727 181.8574892 2.0258161 2.2084787 2.4066192 2.6214652 2.8543391 191.9225013 2.1068491 2.3078603 2.5269502 2.7656458 3.0255995 201.9897888 2.1911231 2.4117140 2.6532977 2.9177563 3.2071355 212.0594314 2.2787680 2.5202411 2.7859625 3.0782329 3.3995636 222.1315115 2.3699187 2.6336520 2.9252607 3.2475357 3.6035374 23 2.2061144 2.4647155 2.7521663 3.0715237 3.4261502 3.8097496 24 2.2833284 2.5633041 2.8760138 3.2250999 3.6145885 4.0489346 252.3632449 2.6658363 3.0054344 3.3863549 3.8133910 4.2918707 26 2.4459985 2.7724697 3.1406790 3.5556726 4.0231279 4.5493829 272.5315671 2.8833685 3.2820095 3.7334563 4.2443999 4.8223459 282.6201719 2.9987033 3.4296999 3.9201291 4.4778419 5.1116867 29 2.7118779 3.1186514 3.5840364 4.1161356 4.7241232 5.4183870 30 2.8067937 3.2433975 3.7453181 4.3219423 4.9839469 5.7434912 312.9050314 3.3731334 3.9138574 4.5380394 5.2580671 6.0881007 323.0067075 3.5080587 4.08998104.7649414 5.5472608 6.4533867 333.1119423 3.6481831 4.2740301 5.0031885 5.8523600 6.8405899 34 3.2208603 3.7943163 4.4663015 5.2533479 6.1742398 7.2510253 35 3.3335904 3.9460889 4.6673478 5.5160152 6.5138230 7.6860868 36 3.4502661 4.1030325 4.9773784 5.7918101 6.8720832 8.1472520 37 3.5710254 4.2680898 5.0368604 6.0814069 7.2500478 8.6360871 383.69601134.4388134 5.3262192 6.3854772 7.6488004 9.1542523 39 3.8253717 4.6163659 5.5658990 6.7047511 8.0694844 9.7035074 40 3.9592597 4.8010206 5.8163645 7.0399887 414.0978337 4.9930614 6.0781009 7.3919881 424.2412579 5.1927838 6.35142407.7615871 434.3897020 5.4004952 6.6375523 8.1496669 444.5433415 5.6165150 6.9362421 8.5571502 10.5464933 12.9854817 45 4.7023585 5.8411756 7.2483730 8.9850077 11.1265504 13.7646107 46 4.8669411 6.0748236 7.57454979.4342581 11.7385217|14.5904873

8.5133060 10.2857178 8.9815378 10.9028608 9.4755224 11.5570325 9.9966761 12.2504547

CASE 1.

The principal, time, and rate given, to find the amount, or interest:

RULE.

Multiply the principal by the ratio involved to the time, (found either by involution, or in table II.) and the product will be the amount; from which subtract the principal, for the compound interest.

EXAMPLES.

1 What will 225 L. amount to in 3 years, at 5 per cent. per annum?

1.05×1.05x1.05-1.157625 raised to the third power; then, 1.157625×225=260 L. 9 s. 3 d. 3 qrs. the Ans. 2. What will 480 L. amount to in 6 years, at 5 per cent. per annum ? Ans. 643 L. 4 s. 11.0178 d. 3. What is the amount of 500 L. at 44 per cent. per annum, for 4 years? Ans. 590 L. 11 s. 5 d. 2.95+qrs. 4. What is the compound interest of a bond for 764 dollars, for 4 years and 9 months, at 6 per cent. per annum? Ans 243 dols. 61 cts+

CASE 2.
DISCOUNT,

Or, the amount, rate, and time given, to find the principal:

Divide the amount by the ratio involved to the time.

EXAMPLES.

1. What principal must be put to interest, to amount to 260 L. 9 s. 3 d. 3 qrs. in 3 years, at 5 per cent. per annum?

260 L. 9 s. 3 d. 3 qrs. 260.465625 1. 1.05x1.05x1.05-1.157625 ratio raised to the 3d

power.

1.157625)260.465625(225 L. Ans.

2. What principal will amount to 547 L. 9 s. 10 d. 2.0528 qrs. in 5 years, at 4 per cent. per annum?

3. What principal will amount to qrs. in 4 years, at 5 per cent.?

3.809

Ans. 450 L. 619 L. 88. 2 d. Ans. 500 L.