TABLE I.

The Amount of one Pound for Years.

Years.

3 per Cent. 3 per Cent. 4 per Cent. 4 per Cent 5 per Cent.

1 1,0300000 1,0350000 1,0400000 1,0450000 1,0500000 21,0609000 1,0712259 1,0816000 1,0920250 1,1025000 3 1,0927270 1,1087178 1,1248640 1,1411661 1,1576250 4 1,1255088 1,1475230 1,1698586 1,1925186 1,2155063 5 1,1592740 1,1876863 1,2166529 1,2461816 1,2762816 6 1,1948523 1,2292553 1,2653190 1,3022601 1,3400956 7 1,2298733 1,2722792 1,3159318 1,3608618 1,407 1004 81,2667700 1,3168090 1,3685691 1,4221006 1,4744554 9 1,3047731 1,3628973 1,4223118 1,4860251 1,5513282 10 1,3439163 1,4105987 1,4862443 1,5529694 1,6288946 11 1,3842338 1,4599697 1,5394541 1,6228530 1,7103393 12 1,4257608 1,5110686 1,6010322 1,6958814 1,7958563 13 1,4685337 1,5639560 1,6650735 1,7721961 1,8856491 14 1,5125897 1,6186045 1,7316764 1,8519449 1,9799376 15 1,5579674 1,6753488 1,8009435 1,9352834 2,0789282 16 1,6017064 1,7339860 1,8729812 2,0223901 2,1828746 17 1,6528476 1,7946755 1,9479005 2,1133768 2,2920183 18 1,7024330 1,8574892 2,0258165 2,2308478 2,4066192 19 1,7535060 1,9225013 2,1068492 2,3078603 2,5269502 20 1,8061112 1,9897888 2,1911231 2,4117140 2,6532977 21 1,8602945 2,0594314 2,2787681 2,5202411 2,7859626 22 1,9161034 2,1315115 2,3699188 2.6336520 2,9252607 23 1,9735865 2,2061144 2,4647155 2,7521663 3,0715238 24 2,0327941 2,2833284 2,5633042 2,8760138 3,2251000 25 2,0937779 2,3632449 2,6658363 3,0054344 3,3863549 26 2,1565912 2,4459585 2,7724697 3,1406709 3,5546527 27 2,2112890 2,5315671 2,8833685 3,2820095 3,7334563 28 2,2879276 2,6201719 2,9987033 3,4296999 3,9201291 29 2,3565655 2,7118779 3,1186514 3,5840364 4,1161336 30 2,4272624 2,8067937 3,2433975 3,7453181 4,3210424

Days.

3 per Cent. per Cent. 4 per Cent. +4 per Cent. 5 per Cent.

11,0000809 1,0000942 1,0001074 1,0001206 1,0001330 21,0001619 1,0001885 1,0002149 1,0002412 1,0002973 31,0002429 1,0002827 1,0003224 1,0003618 1,0004011 41,0003240 1,0003770 1,0004299 1,0004824 1,0005348 5 1,0004050 1,00047,13 1,0005374 1,0006031 1,0006685 61,0004860 1,0005656 1,0006449 1,0007238 1,0008023 7 1,0005670 1,0006600 1,0007524 1,0008445 1,0009361 81,0006480 1,0007542 1,0008600 1,0009652 1,0010699 91,0007291 1,0008486 1,0009675 1,0010859 1,0012037 10 1,0008101 1,0009429 1,0010751 1,0012066 1,0013376 20 1,0016209 1,0011867 1,0021512 1,0024148 1,0026770 30 1,0024324 1,0028315 1,0032288 1,0036243 1,0040182 40 1,0032445 1,0037771 1,0043074 1,0048354 1,0053611 50 1,0040573 1,0047236 1,0053871 1,0060479 1,0067059 60 1,0048708 1,0056710 1,0064680 1,0072618 1,0080525 70 1,0056849 1,0066193 1,0075501 1,0084773 1,0094009 80 1,0064996 1,0075685 1,0086333 1,0096942 1,0107511

J.1990 1,0073151 1,0085186 1,0097177 1,01091251,0121031 100 1,0081311 1,0094696 1,0109803 1,0121324 1,0134563 110 1,0089479 1,0104214 1,0118900 1,0133537 1,0148125 120 1,0097653 1,0113742 1,0129779 1,0145765 1,0161699 130 1,0105834 1,0123279 1,0140670 1,0158007 1,0175291 140 1,0114021 1,0132825 1,0151572 1,0170265 1,0188932 150 1,0122215 1,0142379 1,0162487 1,0182537 1,0202531 160 1,01304151,0151943 1,0173412 1,0194824 1,0216178 170 1,0138623 1,0161516 1,0184350 1,0207126 1.0229843 180 1,0146837 1,0171098 1,0195299 1,0219442 1,0243527 190 1,0155057 1,0180689 1,0206261 1,0231774 1,0257228 200 1,0163284 1,0190288 1,0217233 1,0244120 1,027094 210 1,0171518 1,0199897 1,0228218 1,0256481 1,02846 220 1,0179759 1,0209315 1,0239215 1,0268858 1,0298444 230 1,0188006 1,0219142 1,0250223 1,0281249 1,0312219 240 1,0196260 1,0228778 1,0261243 1,0293655 1,0326013 250 1,0204520 1,0238424 1,02722751,0306076 1,0339825

Case 1. When P, T, and R are given, to find A.

* THEOREM 1. pxrt=A.

By the foregoing tables, thus: Multiply the principal by the tabular number for the given time and rate; and the product will be the amount requiredo T

If the amount be required for any number of years or days that are not in the tables, then observe this rule. Divide the given number of years or days into such numbers as are in the table; then multiply the amounts answering to each, into each other, continually, and the product by the principal, which will be the amount required.

(1) What will 2461. 10s. amount to in 7 years, at 5 per cent.

per annum?

(2) What will 500l. amount to in 30 years and 30 days, at

45 per cent.?

(3) What is the amount of 523l. in 5 years and 194 days, at

5 per cent.?

1

Case 2. When A, R, and T are given, to find P. :

By the foregoing tables, thus: Divide the amount by the tabular number for the given time and rate, and the quotient

will be the principal required.

EXAMPLES.

(4) What principal, or sum of money, must be put out to

* The most convenient way of giving the four Theorems in

Compound Interest is by Logarithms, as follows:

1. txlog.r+log.p=log.A.1
2. log.a-t x log.r=log.P.

log.a-log.p.

3.

=T.

raise a stock of 2431. 2s. d. in 4 years, at 5 per cent, per annum ?

(5) What principal, being put to interest, will amount to 3461. 17s. in 7 years, at 5 per cent. per annum? (6) What principal, being put to interest for 30 years at 44 per cent. per ann, will amount to 1872l. 13s. 2d.? (7) What principal, being put to interest for 5 years and 194 days, will amount to 6851. 71⁄2d. at 5 per cent. per annum?

Case 3. When P, A, and R are given, to find T.

!

THEOREM 3.2 R.

a

9

{

A

Which being continually divided by r, till nothing remains, the number of those divisions will be equal to T, the time.

By the foregoing tables, thus: Divide the amount by the principal, and the quotient will be the amount of 11. at the given rate, which will be found under the rate, even with the time required.

EXAMPLES.

(8) In what time will 2461. 10s. amount to 3461. 17s. at 5 per cent. per annum ?

(9) In what time will 530/. amount to 1872l. 13s. 2d. at 4

per cent. per annum ?

:

;

(10) In what time will 510l. amount to 6851. 74d. at 5 per cent. per annum ?

Case 4. When A, P, and T are given, to find R.

1

By the foregoing tables, thus: Proceed as with the last, and even with the given time is under the rate required.

EXAMPLES.

(11) At what rate per cent. will 2461. 10s. amount to 3461. 17s. in 7 years?

(12) At what rate per cent. will 500l. amount to 18721.

13s. 2d. in 30 years?

(13) At what rate will 5231. amount to 6851. 71⁄2d. in 5 years and 195 days?

LXVIII. ANNUITIES, PENSIONS, in ARREARS.

HERE U represents the annuity, pension, or yearly rent, A, R, and T, as before.

The 3d Table shows the amount of 11. annuity for any number of years, under 31, at 3, 34, 4, 45 and 5 per cent. and is thus constructed: Take the first year's amount, which is 11., multiply by 1,05+1=2,05=2d year's amount; which also multiply by 1,05+1=3,1525=3d year's amount.

The 4th Table shows the present worth of 14 due at any number of years, to commence under 31, rebate at 3, 3, 4, 44, and 5 per cent. and is made thus: 1÷1,05-952381 first year's present worth, and 952381-1,05=9070295= 2d year's, and 907031,05,8638376, the third year's present worth, &c.