(57) What is the present worth of 1000l. due at 5 months, at

4 per cent.?

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

Case 21. When P, T, and R are given, to find S.
THEOREM 20. ptr+p=S.

EXAMPLES.

(59) Suppose I receive 1447. 11s. 6d. 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.

(60) If the present worth of a sum of money due 5 months hence, allowing 44 per cent. be 981l. 10s. 5d. what was the sum first due?

(61) A person paid 91111. 3s. 84d. 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.

(62) The present worth of 1501, due for a certain time to come, is 1441. 12s. 6d. at 5 per cent. I demand in what time the first sum should have been paid, if no rebate had been made.

(63) A person receives 9811. 10s. 5d. for 10001. due at a certain time to come, allowing 44 per cent. discount. I

desire to know in what time the debt should have been discharged without any rebate.

(64) I have received 91117. 3s. 84d, for a legacy of 93421. allowing the executor 4 per cent. I demand when the legacy was payable without rebate.

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

EXAMPLES.

(65) At what rate per cent, will 150l. payable 9 months hence, produce 1441. 11s. 6d. for the present pay

ment?

(66) At what rate per cent. will 10001. payable at 5 months hence, produce 9811. 10s. 5d. for the present payment?

(67) At what rate per cent. will 93427. payable, 10 months hence, produce 91111. 3s. 84d. for the present pay

ment?

1. Find the present worth

of each payment for its Thus, THEOREM 23.

respective time.

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

(68) D. owes C. 14007. which was to have been paid as follows: 400l. down; 500l. at the end of 6 months; 250l. at the end of 8 months, and the rest at the end of 10 months; but they agree to have but one payment of the whole, rebate at 3 per cent. The true equated time is demanded.

(69) In what time will the interest of 491. 3s. equal the proceed of 121. 6s. of use 47 days, at any rate of in

terest?

(70) Put out 3847. to interest, and in 8 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 11. for 1 year, at any given rate which is found by the following proportion.

Thus,

As

100 105

{100

1 1,05

R, at 5 per cent.

100: 106 1: 1,06 = R, at 6 per cent., &c.

The construction of the first table following, showing the amount of 11. for any number of years under 31, at 3, 31, 4, 4, and 5 per cent.

Thus the amount of 11. for 2 years, at 5 per cent. compound interest, will be 1,05 × 1,05=1,025.

Also, 1,05 × 1,05 × 1,05=1,157625 the amount of 17. for 3 years, at 5 per cent.

And the construction of the second table is by the continual multiplication of the amount of 17. for a day; the amount of 11. for a day being the root of its amount for a year, extracted to the 365th power.

The amount of 11. for a day at 5 per cent. is 1,0001336, its amount for 2 days will be 1,0001336 × 1,0001336, = 1,0002672, &c. and 1,0001336 x 1,0001336 × 1,00013361,0004011, the amount of 17. at 5 per cent. for 3 days, compound interest.

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.

11,0300000 1,0350000 1,0400000 1,0450000 1,0500000 2 1,0609000 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 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 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 2,3078608 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 1,9735265 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

TABLE II.

The Amount of one Pound for Days.

Days.

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

1 1,0000809 1,0000942 1,0001074 1,0001206 1,0001330 2 1,0001619 1,0001885 1,0002149 1,0002412 1,0002973 3 1,0002429 1,0002827 1,0003224 1,0003618 1,0004011 4 1,0003240 1,0003770f 1,0004299 1,0004824 1,0005348 51,0004050 1,0004713 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 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 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 1,0109125 1,0121031

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 1,0270949 210 1,0171518 1,0199897 1,0228218 1,0256481 1,0284687 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| 1,0272275) 1,0306076) 1,0339825|