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.

Rate

per

TABLE 1.

Amounts of L. 1 for a year and for
quarters, at Compound Interest.

cent. Ratio. For 3 qrs. For 2 qrs. For 1 qr.

Simp. Int. of L. 1 for 1 month.

5

50

1.045 1.033563 1.022252 1.011065
1.05 1.037270 1.024695 1.012272
1.055 1.040973 1.027132 1.013475

.003750

.004167

.004583

6

1.06 1.044671 1.029536 1.014674 61 1.065 1.048364 1.031988 1.015868)

.005000

.005417

7

1.07 1.052053 1.0344081.017058||

.005833

The ratio involved to the time is the amount of 1L. or dollar for the time given; as a square for 2 years, a cube for 3, &c. thus, 1.06x1.06×1.06×1.06.

4

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 4 years, &c.

The power or the amount of 1L. or dollar, may also be obtained for months and days (nearly) by adding the monthly simple interest of IL. 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,

=1.029563: For 4 yrs. = 1.318873

Amount for yr.
Int. of 1L. for 1mo.
One sixth for 5dys.

.005000

.005000 .000833

For 7mo. 5dys.=1.035396: For 4 years, 10mo. 5dys.=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 1L. or Dollar

from 1 year to 46.

4 per 5 per

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

1.1087178 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 61.22925531.2653190 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 91.36289731.4233118 1.4860951|1.5513282 1.6190939 1.6894789 10 1.4105987 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 1.8356491 2.0057732 2.1329282 141.6186945 1.7316764 1.8519449|1.9799316 2.1160907 2.2609039 15 1.6753483 1.8009435 1.9352824 2.0789281 2.2324756 2.3965581 161.7339860 1.87298122.0223701 2.1828745 2.3552617 2.5403517 171.7946755 1.9479005 2.1133768 2.2920183 2.4848011 2.6927727) 18 1.85748922.0258161 2.2084787 2.4066192 2.6214652 2.8543391 19 1.92250132.1068491 2.3078603 2.5269502 2.7656458 3.0255995 20 1.98978882.1911231 2.4117140 2.6532977 2.9177563 3.2071355 212.0594314 2.2787680 2.5202411 2.7859625 3.0782329 3.3995636 222.13151152.3699187 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 2.4459985 2.7724697 3.1406790 3.5556726 4.0231279 4.5493829 27 2.5315671 2.8833685 3.2820095 3.7334563 4.2443999 4.8223459 282.6201719 2.9987033 3.4296999 3.9201291 4.4778419 5.1116867 29 2.71187793.1186514 3.5840364 4.1161356 4.7241232 5.4183870 30 2.8067937 3.2433975 3.7453181 4.3219423 4.9239469 5.7434912 312.9050314 3.37313343.91385744.5380394 5.2580671 6.0881007 323.0067075 3.5080587 4.0899810 4.7649414 5.5472608 6.4533867 333.11194233.64818314.2740301 5.0031885 5.8523600 6.8405899 343.22086033.7943163 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 4.87737845.7918101 6.8720832 8.1472520 37 3.5710254 4.2680898 5.0968604 6.0814069 7.2500478 8.6360871 383.69601134.43881345.32621926.3854772 7.6488004 9.1542523 39 3.82537174.6163659 5.5658990 6.7047511 8.0694844 9.7035074 403.95925974.8010206 5.8163645 7.0399887 8.5133060 10.2857178 41 4.09783374.99306146.0781009 7.3919881 8.9815378 10.9028608 424.24125795.1927838 6.3514240 7.7615871 9.4755224/11.5570325 434.38970205.40049526.63755238.1496669 9.9966761 12.2504547 44 4.54334155.6165150 6.9362421 8.5571502 10.5464933 12.9854817 45 4.7023585 5.8411756 7.2483730 8.9850077 11.1265504 13.7646107 464.8669411 6.0748236 7.5745497 9.4342581 11.7385217 14.5904873

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. per annum? Ans. 643L. 4s. 11.0178d. 3. What is the amount of 500L. at 44 per cent. per annum, for 4 years? Ans. 590L. 11s. 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. 243dols. 61cts. +

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.=260.465625L. 1.05×1.05×1.05-1.157625 ratio raised to the 3d

power.

1.157625)260.465625(225L. Ans.

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

Ans. 450L. 3. What principal will amount to 619L. 8s. 2d. 3.809

qrs. in 4 years, at 51⁄2 per cent.?

Ans. 500L.

An annuity is a sum of money payable yearly, half yearly, or quarterly, for a number of years, during life, or for ever; and may draw interest if it remain unpaid after it becomes due.

Tables to facilitate the calculations of annuities.

TABLE III.

Showing the amount of 1L. annuity.

Y4 per ct. 4 per ct. 5 per ct. 5 per ct. 6 per ct. Y

9 10.582795 10.802114 11.026564 11.256259 11.491316 9 10 12.006107 12.28821 12.577892 12.875354 13.18079510] 11 13.486351 13.841179 14.206787 14.583498 14.971643 11 12 15.025805 15.464032 15.917126 16.38559 16.869942 12 13 16.626838 17.159913 17.712983 18.286798 18.882138 13 14 18.291911 18.932109 19.598632 20.292572 21.015066 14 15 20.023588 20.784054 21.578563 22.408663 23.275971 15 16 21.824531 22.719337 23.657492 24.64114 25.672528 16 17 23.697512 24.741707 25.840366 26.996402 28.212881 17 18 25.645413 26.855084 28.132385 29.481205 30.905653 18 19 27.671229 29.063562 30.539004 32.102671 33.75999319 20 29.778078 31.371423 33.065954 34.868318 36.785592 20 21 31.969202 33.783137 35.719252 37.786075 39.99272821 22 34.247970 36.833378 38.505214 40.864309 43.392291 22 23 36.617888 38.93703 24 39.082604 41.689196 25 41.645908 44.56521 26 44.311745 47.570645 51.113454 54.965979 59.156383 26 27 47.084214 50.711324 54.669126 58.989109] 63.705766 27 28 49.967582 53.993333 58.402583 63.23351 68.528117 28 29 52.966286 57.423033 62.322712 67.711353 73.639798 29 30 56.084938 61.007069 66.438847 72.435478 79.058186 30 31 59.328335 64.752388 70.76079 77.419429 84.801677 31 32 62.701469 68.666245 75.298829 82.677498 90.889778 32 33 66.209527 72.756226 80.063771 88.22476 97.343165 33 34 69.857904 77.030256 85.066959 94.077122 104.183754 34 35 73.652225 81.496618 90.320307 100.251363 111.434780 35 36 77.598314 86.163966 95.836323 106.765188 119.120867 36 37 81.702246 91.041344 101.628139 113.637274127.268118 37 38 85.970336 96.138205 107.709546 120.887324 135.904206 38) 39 90.40915 101.464424 114.095023 128.536127 145.058458 39 40 95.025516 107.030329 120.799774 136.605146 154.761966 40

41.430475 44.111846 46.995828 23 44.501999 47.537998 50.815578 24 47.727099 51.152588 54.864513 25