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(57) What is the present worth of 10001. due at 5 months, at

41 per cent. ? (58) What is the discount of 93421. at 4 per cent, for 10

months ?

Cuse 21. When P, T, and R are given, to find S.

THEOREM 20. ptr +p=S.

EXAMPLES. (59) Suppose I receive 1441. 11s. 6 d. now, for a sum of

money due 9 months 'hence, allowing 5 per cent. for present payment, I demand the sum that was due at

first. (00) If the present worth of a sum of money due 5 months

hence, allowing 45 per cent. be 981l. 10s. 5d. what

was the sum first due? (61) A person paid 1111. 38. 8d, for a debt due 10 months

hence, he being allowed 4 per cent. for the discount, How much was the debt?

Case 22. When S, P, and R are given, to find T.
Theoreu 21.92=T.

por

EXAMPLES (62) The present worth of 1501, due for a certain time to

come, is 1441. 128. 6 d. at 5 per cent. I demand in what time the first sum should have been paid, if no rebate

had been made. (69) A person receives 9811. 10s. 5d. for 10001. due at a cer

tain time to come, allowing 45 per cent. discount. I desire to know in what time the debt should have been

discharged without any rebate, (64) I have received 91111. 3s. 8d, for a legacy of 93421.

allowing the executor 4 per cent. I demand when the Jegacy was payable without rebate.

Case 23. When S, P, and T are given, to find R.

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EXAMPLES

(65) At what rate per cent, will 1501. payable 9 months

hence, produce 1441. 11s. 6 d. for the present pay

ment? (66) At what rate per cent. will 1000l. payable at 5 months

hence, produce 9811. 10s. 5d. for the present pay

ment? (67) At what rate per cent. will 93421. payable 10 months

hence, produce 91111. 38. 8 d. for the present payment?

LXVI. EQUATION of PAYMENTS. TO find the equated time for the payment of any sum of money, due at several times,

RULE.

1. Find the present worth

of each payment for its Thus, THEOREM 23. =P respective time.

tr+1 2. Add all the present worths together, and call that sum P;

then wills-p=D, the rebate,

d 3. Add -=E, the true equated time.

pr

EXAMPLES.

(68) D. owes C. 14001. which was to have been paid as fol

lows: 4.001. down ; 5001. at the end of 6 months; 2501. at the end of 8 months, and the rest at the end of 10 months; but they agree to have but one páyment of the whole, rebate at 3 per cent. The true equated time is demanded.

(69) In what time will the interest of 491. 38. equal the

proceed of 121. os. of use 47 days, at any rate of in

terest ? (70) Put out 3841. to interest, and in 84 years there were

5421. 8s. found to be due. What rate of interest could then be implied?

LXVII. COMPOUND INTEREST.

The letters, made use of here are,

A, the amount.
P, the principal.
T, the time.
R, the amount of il. for 1 year, at any given rate

which is found by the following proportion.

Thus,

As

100 : 105 :: 1: 1,05 = R,

at 5
per

cent.
100 : 106 :,

The construction of the first table following, showing the amount of il, for any number of years under 31, at 3, 3, 4, 44, and 5 per cent.

Thus the amount of 1l. for 2 years, at 5 per cent. compound interest, will be 1,05 x 1,05 =1,025, Also, 1,05 x 1,05 x 1,05=1,157625=the amount of 11. for 3

years, at 5 per cent. And the construction of the second table is by the continual

multiplication of the amount of 11. for a day; the amount of ll.' for a day being the root of its anjount for a year,

extracted to the 3651h power. The amount of ll. for a day at 5 per cent. is 1,000 1336,

its amount for 2 days will be 1,0001336 x 1,0001336, = 1,0002672, &c. and 1,0001336 x 1,0001336 x 1,0001336=1,0004011, the amount of 1l, at 5 per cent. for 3 days, compound interest.

TABLE I.

The Amount of one Pound for Years.

Years.

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

1,0300000 1,0350000 1,0400000 1,0450000 1,0500000 2 1,0609000 1,0712259 1,0816000 1,09202501,1025000 3 1,0927270 1,1087178 1,1248640) 1,1411661 1,1576250 4 1,125508 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 1,3608619 1,4071004 8 1,2667700 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 u 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 1,51258971 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 171 1,6528476 1,7946755 1,9479005 2,1133768 2,2920183

18 1,7024330 1,8574892 2,0258 165 2,2308478 2,4066192 191 1,7535060/ 1,9225013 2,1068492 2,30786032,5269502 20 1,8061112 1,9897838 2,1911231| 2,4117140 2,6532977 121 1,8602945 2,0594314 2,2787681 2,5202411 2,7859626 22 1,9161034 2,1315115 2,3699188 2.6336520 2,9252607 23 1,9735265 2,2061144 2,4647155 2,7521663 3,07 15238 241 2,0327941| 2,2833284 2,5633042 2,8760138 3,2251000

25 2,0937779 2,3632449 2,6658363 3,0054344 3,3863549 126 2,1565912 2,4459585 2,7724697) 3,1406709 3,5546527 27] 2,2112890 2,5315671| 2,8833685 3,2820095 3,7334563 24 2,2879276 2,6201719 2,9987033 3,4296999 3,920129) 29 2,3565655 2,7118779| 3,1186514 3,58403641 4,1161336 304 2,4272624) 2,8067937) 3,2433975/ 3,74531811 4,3210424

TABLE II.
witin 1 16
The Amount of one Pound for Days.

Days.

per Cent. \\ per Cent 4 per Cent. +1 per Cent. 5 per

Cent.

il 1,0000809{ 1,0000942 1,0001074 1,0001206 1,0001330 2) 1,0001619) 1,0001885/ 1,0002149 1,0002412 1,0002973 3/ 1,00024291 1,0002827 1,0003224 1,00036181 1,0004011 4 1,0003240 1,0003770f 1,0004299 1,0004824 1,0005348 51:1,0004050) 1,0004713 1,0005374/ 1,0006031 1,0006685 61.1.0004860 -1,0005656) 1,0006449/ 1,0007238 1,0008023 7/ 1,0005670 1,0006600 1,0007524 1,0008445) 1,0009361 8 1,0006489 1,0007542 1,0008600 1,0009652 1,0010699 9 1,0007291 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 301 1,00243244 1,0028315 1,0032288 1,0036243 1,0040182 40 1,0032445/ 1,0037771 1,0043074| 1,0048354 1,0053611 501 1,0040573 1,0047236 1,0053871| 1,0060479 1,0067059 601 1,0048708 1,0056710 1,0064680 1,0072618 1,0080525 70 1,0056849) 1,0066193) 1,0075501 1,0084773, 1,0094009 801 1,0064996 1,0075685 1,0086333) 1,0096942 1,0107511

90 1,0073151 1,0085186 1,00971771 1,0109125, 1,012103) 100 1,0081311 1,0094696 1,0109803 1,0121324 1,0134563 110 1,0089479 1,01042141 1,0118900 1,0133537| 1,0148125) 120 1,0097653 1,0113742 1,0129779 1,0145765/ 1,0161699 1301 1,0105834 1,0123279| 1,0140670 1,0158007 1,0175291 1401 1,01140211 1,0132825 1,0151572 1,0170265/ 1,0188932 1150 1,0122215 1,0142379 1,0162487 1,0182537| 1,0202531 1760f 1,01304157. 1,0151943f 1,01734121 1,01948241 1,0216178 1701 1,0138623 1,0161516| 1,0184350 1,0207 126 1.0229843 180 1,01468371,0171098| 1,0195299 1,0219442 1,0243527 190 1,0155057| 1,0180689 1,0206261 1,0231774 1,0257228 200 1,0163284| 1,01902881 1,0217233 1,0244 120 1,0270949 210 1,01715181 1,0199897 1,0228218 1,0256481 1,0284687 1220 1,01797591 1,0209315 1,02392151 1,0268858 1,0292444

230 1,0188006 1,0219142 1,0250223 1,0281249 1,0312219 1240 1,0196260 1,0228778 1,02612431 1,0293655 1,0326013 2501 1,02045201 1,02384241 1,02722751 1,03060761 1,0339825

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