Εικόνες σελίδας
PDF
Ηλεκτρ. έκδοση

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

* Theorem 1. pxmt=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 each, into each other, continually, and the product by the principal,

SLO which will be the amount required.

EXAMPLES (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

41 per cent. ? (3) What is the amount of 5231, in 5 years and 194 days, at

5 per cent. ?

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

A

=P. THEOREM 2. R 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. tx log.r+log.p=log. A. 2. log.amtx log.r=log.P.

log. a-log.p.
3.

=T.
log. r.
log.a-log p.

-=log. R.

[ocr errors]

i raise a stock of 2431. 2s. Id. in 4 years, åt :5 per cent,

per annum ? (5) What principal, being put to interest, will camount to

3461. 17s. in 7 years, at 5 per cent. per annum: (6) What principal, being put to interest for 30 years at 41

per cent. per ann, will amount to. 18721. 138. 2d. ? (7) What principal, being put to interest for 5 years and 194

days, will amount to 6851,7 d. at 5 per cent. per annum?

[ocr errors]
[ocr errors][ocr errors]

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

Which-being continually divided THEOREM 3. -=R.

byr, 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 ll. 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 wili 5301. amount to 18721. 13s. 2d. at 41

per cent. per annum? (10) In what time will 5101, amount to 6851. 71 d. at 5 per

cent. per annum?

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

[ocr errors]

Which being extracted by the

rules of Extraction (the time THEOREM 4. =Rt. P

given to the question showing the

power) will give the rate. 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. ?

138. 2d. in 30 years? (13) At what rate will 5231. amount to 6851. 7{d. 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 sh ws the amount of il. annuity for any number of years, under 31, at 3, 34, 4, 4 and 5 per cent. and is thus constructed: Take the first year's amount, which is 11., multiply by 4,05+1=2,05–20 year's amount; wbich also multiply by 1,05 +1=3,1525=3d year's amount.

The 4ih Table shows the present worth of 12 due at any number of years, to commence under 31, rebate at 3, 31, 4, 41, and 5 per cent, and is made thus: 11,05=952381 first year's present worth, and ,952381–1,05=9070295= 20 year's, and ,90703 - 1,055,8638376, the third year's present worth, &c.

[ocr errors]

TABLE III.

The Amount of One Pound per Annum, or. Annuity, for

Years.

Years

3 per Cent. 31 per Cent. 4 per

Cent. 41 per

Cent. 5 per Cent.

1,0000000 1,0000000 1,0000000 1,0000000 1,0000000 2 2,0300000 2,0350000 2,0400000 2,0450000 2,0500000 3 3,0909000 3,10622501 3,1216000 3,1370260 3,1525000 44,18362704,2149429 4,24646401 4,2781911 4,3101250 55,3091358 5,3623659 5,4707097 5,4707097 5,5256312 66;4684099 6,5501522 6,6329755 6,71689176,0019128 77,6624622 7,7794075 7,8982943 7,0191518 8,1420081

8,89233609,0516866|9,2142263 9,3800136| 9,5493643 910,1591061/10,3684958 10,5827953|10,8021142 11,0267871 10 11,463879311,7313931|12,0261071|12,2882094 12,577 1925 1112,8077957|13,14)9919 13,486351413,8411788|14,2067871 12114,1920296 14,6019616|15,0258055|15.4640319 15,9171265 13/15,617790416,1130303|16,6262397|17,1599133 17,7129828 1417,086324217,6769864|18,291911218,9321094|19,5986320 15 18,5989139|19,2956809|20,0235276 20,7840543|21,5785636 16 20,156881320,9710297|21,824531122,7193367 23,6574918 |07|21,7615877 22,7050158|23,6975124/24,741706925,8403664 11823,414435424,499691225,6454129 26,8550837 28,1323841 1925, 1168634/26,3571805 27,67 12294 29,0635625|30,5390039 |2026,8703745 28,27968 18|29,778078631,371422|33,0659547 121 28,6764857 30,2694707131,969201733,783130*35,7192518 122 30,5367803|32,3289022|34,2479698 36,503377939,5052144 23 32,4528837 34,4604137 36,617888638,0370299 41,4304651 P4\34,4264702 36,6665282|39,0826041 41,6891963-14,5019989 25 36,4592643|38,949856741,6459083 44,5652 101 47,7270988 126 38,5530422 41,3131017 44,3117440 47,570644651, 134538 27 40,7096335/43,7590602 47,0842144|50,7113236 54,6691265 28142,9309225/46,2906273 49,9675830153,993333258,4025828 2945,2188502 48,910799352,9662863 57,423033262,3227 119 \30147,5754157151,6226773156,0849277161,0070607166,4388475

TABLE IV.

[ocr errors]

The Present Worth of one Pound for Years.

Years.

3
per

Cent. 34 per Cent. 4 per Cent. 41 per Cent. 5 per cent.

1,9708738 ,9661836 ,9615385 ,9569378 ,9523809 2,9425959 ,9331507 ,9245562 ,9157299

,9070295 3 ,9151417 ,9019427 ,8889964 ,8762966 ,8638376 4,8884870 ,8714422 ,8548042 ,8385613 ,8227025 5) ,8626088 ,8419732 ,8219271 ,8024511 ,7835262 61 ,8374843 ,8135006 ,7903145 ,7678957 ,7462154 7,8130915 ,7859910 ,7599178 ,7348285 ,7106813 8,7894092 ,7594116 ,7306902 ,7031851 ,6768394

9 ,7664167 ,7337310 ,7025867 ,6729044 ,6446089 101 ,7440939 ,7809183,6755642,6439277 ,6139133 111,7224213 ,6849457 ,6495809,6161988 ,5846703 12,7013799 ,6617833 ,6245971 ,5896639 ,5568374 13 ,6809513,6394041,6005741 ,5642716 ,5303214 14,6611178 ,6177818,5774751 1,5399729 ,5050679 15 ,6418619 ,5968906 ,5552645 ,5167204 ,4810171 16 ,6231669 ,5767059 ,5339082 ,4944693 ,4581115 1171,6050164 1,7572038 ,5133733 ,4731764 ,4362967 18 ,5873846,5383611,4936281 ,4528004 ,4155207 19 ,5702960 ,5201577 ,4746424 ,4333018 ,3957340 20 ,5536758 ,5025659,4563870 ,4146429 ,3768895 211 ,5375493 ,4855709 ,4388336 ,3967874 ,3489424 22 ,5218925 ,4691506 ,4219554 ,3797009 ,3418479 231 ,5066917 ,4532856,4057263 ,3633501 ,32557 13 24 ,4919337 ,4379571 ,3901215 ,3477035 ,3100639 25 ,4776056,4231470 ,3751168,3327306 ,2953028 26 ,4636947 ,4088378 ,3606892 ,3184025 ,2812407 27,4501891 ,3950123 ,3468166 ,3046914 ,2678483 128,4370768 ,3816543 ,3334775 ,2915707 ,2550936 29,4243464 ,3687482 ,3206514 ,2790150 ,2429463 301 ,4119868 ,3562784 1,3083187 ,2670000 2315775

« ΠροηγούμενηΣυνέχεια »