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

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

Ans.

{

8947848L. 10s. 6d. Amount. 298261L. 12s. 4d. 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 100L. per yard?

Received 214469929L. 5s. 31d. 214466929L. 5s. 31d.

Ans.Gained

5. A goldsmith sold 1 lb. of gold, at a farthing for the first ounce, a penny for the second, 4d. 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 4L, per ounce for the gold?

S He received 5825L. 8s. 51d. Ans. And gained 5777L. Ss. 54d.

5. 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. dou bling to the last? Ans. 4473924L. 5s. 31d.

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 dols.

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 2s. 6d. per bushel? Ans. 1773L. 7s. 6J

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 100 1: 105: 1.05 As 100: 1 :: 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.

31/12 1.035 1.026137 1.017349 1.008637 .002917

4 1.04 1.029852 1.019804 1.009853 .003333 41 1.045 1.033563 1.022252 1.011065 .003750

6

5 1.05 1.037270 1.024695 1.012272 .004167 54 1.055 1.040973 1.027132 1.013475 .004583 1.06 1.044871 1.029536 1.014674 .005000 61 1.065 1.048364 1.031988 1.015868 .005417 1.07 1,052053 1.034408 1.017058 .005833j

7

The ratio involved to the time is the amount of iL. or

dol. for the time given; as a square for 2 for 3, &c. thus, 1.06 × 1.06 × 1.06 × 1.06.

years,

cube

or 1.06

4

1.262477

nvolved to 4 years.

the 4th power of 1.06, or the ratio

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, 1.262477x 1.044671: 1.318873 for 43 years, &c.

The power or the amount of 1 L. or dol. may also be obtained for months and days (nearly) by adding the monthly simple interest of 1 L. 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 1L. for 1 mo.=
One sixth for 5 dys.

For 7 mo. 5 dys.

1.035396: For 4y. 10mo. 5d.-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. Shewing the amount of 1 L. or Dollar, from 1 year to 45.

year

3 per 4 per 14 per | 5 per 5 per 6 per

cent.

cent. cent. cent.

cent. cent.

11.0350000 1.0400000 1.0450000 1.0500000 1.0550000 1.0600000 21.0712250 1.0816000 1.0920250 1.1025000 1.1130250 1.1360000 31.1087178 1.1248640 1.14116611.1576250 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 .3788426 1.4185191 71.2722792 1.3159317 1 3608618 1.4071004 1.4546789 1.5036302 8/1.3168090 1.3685690 1.4221006 1.4774554 1.5345862 1.5938480 91.3628973 1,4233118 1.4860951 1.5513282 1.6190939 1.6894789 10 1.41059871.4802442 1.5529694 1.6238946 1.7081440 1.7903476 111.4599697 1.5394540 1.6228530 1.7103393] 1.8020919) 1.8982985 12 1.5110686 1.6010322 1.6958814 1.7958563 1.9012069 2.0121964 13 1.5630560 1,6650735 1.7721961 1.8856491 2.0057732 2.1329282 14 1.6186945 1.73167641.8519449 1.9799316) 2.1160907 2.2609039 15 1.6753488 1.8009435 1.9352824 2.0789281 2.2324756 2.3965581 16/1.7339860 1.87298122.0223701 2.1828745 2.3552617 2.5403517 171.7946755 1.9479005 2.1133768 2.2920183 2.4848011 2.6927727 18 1.8574892 2.0258161 2.2084787 2.4066192 2.6214652 2.8543391 19 1.9225013 2.1068491 2.3078603 2.5269502 2.7656458 3.0255995 20 1.9897888 2.1911231 2,4117140 2.6532977 2.9177563 3.2071355 212.0594314 2.2787680 2.5202411 2.7859625 3.0782329 3.3995636 22 2.1315115 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 25 2.3632449 2 6658363 3.0054344 3.3863549 3.8133910 4.2918707 26 2.44599852.7724697 3.1406790 3.5556726 4.0231279 4.5493829 27 2.5315671 2 8833685 3.2820095 3.7334563 4.2443999 4.8223459 28 2.6201719 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 8057937 3.2433975 3.7453181 4.3219423 4.9839469 5.7434912 31 2.9050314 3.3731334 3.9138574 4.5380394) 5.2580671 6.0881007 3213.0067075 3.5080587 4.0899810 4.7649414) 5.5472608 6.4533867 33 3.1119423 3 6481831 4.2740301 5.0031885 5.8523600 6,8405299 34 3.2208503 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 4.8773784 5.7918101 6.8720832 8.1472520 37 3.5710254 4.2680898 5.0968604 6.0814069 7.2500478 8.6360871 38 3.6960113 4.4388134 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 8.5133060 10.2857178 41 4.0978337 4.9930614 6.0781009 7.3919881 8.9815378 10.9028608 42 4.2412579 5.1927838 6.3514240 7.7615871 9.4755224 11.5570325 43 4.3897020 5.4004952 6.6375523 8.1496669) 9.9966761 12.2504547 44 4.5433415 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 6.07482367.574549719.4342581|11.738521714.5904873

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

1.05 × 1.05 × 1.05–1.157625 raised to the third power; then, 1.157625 × 225-260L. 9s. 3d. 3qrs. the Ans. 2 What will 480L. amount to in 6 years, at 5 per cent. Ans. 643L. 4s. 11.0178d. per annum? 3. What is the amount of 500L. at 44 per cent. per ann. for 4 years? Ans. 590L. 118. 5d. 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 duls. 61 cts.+

CASE 2.
DISCOUNT,

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

RULE.

Divide the amount by the ratio involved to the time.

EXAMPLES.

1. What principal must be put to interest, to amount to 260L. 9s. 3d. 3qrs. in 3 years, at 5 per cent. per annum ? 260L. 9s. 3d. 3qrs. 260.4f5625L.

1.05x1.05x1.05-1.157625 ratio raised to the 3d power 1.157625)260.465625(225L. Ans.

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

Ans 450L. 3. What principal will amount to 619L. 8s. 2d. 3.808 qrs. in 4 years, at 5 per cent. ? Q ?

Ans. -OOL.