60.

REBATE

or

DISCOUNT.

Here S reprefents the Sum to be discounted, P the present Worth, T and R as before.

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

E X. A MP LE S.

56. What is the prefent Worth of 150l. due 9 Months hence, at 5 per Cent.?

57. What is the present Worth of 1000l, due at 5 Months

at 4 per Cent. ?

58. What is the Discount of 93427. at 4 per Cent. for 10 Months?

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

THEOREM 20. prp=S.

E X A M

PLES.

59. Suppofe I receive 1441. 115. 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 41 per Cent. to be 9817. 10s. 5d. what was the Sum firft due?

61. A Perfon paid 9111l. 35. 8d. for a Debt due 10 Months hence, he being allowed 4 per Cent. for the Discount, how much was the Debt?

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

62. The prefent Worth of 150l. due for a certain Time to come is 144/. 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 Perfon receives 9817. 10s. 5d. for 100l. due at a certain Time to come, allowing 4 per Cent. Discount; I defire to know in what Time the Debt should have been discharged without any Rebate?

64. I have received 91111. 35. 8d. for a Legacy of 93421. allowing the Executor 4 per Cent. I demand when the Legacy was payable without Rebate?

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

EXAMPLE S.

65. At what Rate per Cent. will 150l. payable 9 Months hence, produce 144/. 11s. 6d. for the prefent: Pay

ment?

66. At what Rate per Cent. will 1000l. payable at 5 Months hence, produce 9817. 10s. 5d. for the present Payment?

67. At what Rate per Cent. will 93427. payable 10 Months hence, produce g111l. 35, 8d. for the prefent Payment?

61

EQUATION of PAYMENTS.

To find the equated Time for the Payment of any Sum of Money, due at several Times.

refpective Time.

Thus Theorem 23.P.

tri

2. Add all the prefent Worths together, and call that Sum P, then will's-p=D, the Rebate.

d

3. And E, the true equated Time.

pr

68. B. owes C. 1400l. which was to have been paid as follows; 400/. down, 500l. at the End of 6 Months, 250l. at the End of 8 Months, and the Reft at the End of 10 SJSAT Months;

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 Intereft of 491. 35. equal the Proceed of 127. 6s. at Ufe 47 Days, at any Rate of Intereft?

70. Put out 3841. to Intereft, and in 84 Years there were 5421. 8s. found to be due; what Rate of Intereft could then be implied?

62. COMPOUND INTEREST.

The Letters made use of here, are,

A, the Amount.

P, the Principal.

T, the Time.

I

R, the Amount of l. 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 I: 1,06 R, at 6 per Cent. &c.

The Conftruction of the firft Table following, fhewing 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 Integers, will be 1,05×1,05=1,1025.

Alfo,

1,05X1,05X105=1,157625=the Amount of 11. for 3 Years, at 5 per Cent.

And the Conftruction of the fecond Table is by the Continual Multiplication of the Amount of 17. for a Day; the Amount of 17. for a Day being the Root of its Amount for a Year, extracted to the 365th Power. The Amount of 17. for a Day at 5 per Cent. is 1,0001336, its Amount for 2 Days will be 1,0001336X1,0001336 1,0002672, &c. and 1,0001336X1,0001336X 1,0010336=1,0004011, the Amount of 17. at 5 per Cent. for 3 Days compound Interest.

TABLE

TABLE I.

The Amount of One Pound for Years.

Years.

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

1,0500000 1,102 5000 1,1576250

1,2155063

1,2762816

1,3400956 1,4071004 1,4744554 1,5513282 1,6288946 1,7103393 1,7958563

I 1,0300000 1,0350000 1,0400000 1,0450000 2 1,0609000 1,0712250 1,0816000 1,0920250 3 1,0927270 1,1087178 1,1248640 1,1411661 4 1,1255088 1,1475230 1,1698586 1,1925186 51,1592740 1,1876863| 1,2166529 1,2461816 61,1948523 1,2292553 1,2653190 1,3022601 7 1,2298733 1,2722792 1,3159318 1,3608618 81,2667700 1,3168090 1,3685691 1,4221006 91,3047731 1,3628973 1,4223118 1,4860251 10 1,3439163 1,4105987 1,4862443 1,5529694 11 1,3842338 1,4599697 1,5394541 1,6228530 12 1,4257608 1,5110686 1,6010322 1,6958814 13 1,4685337 1,5639560 1,6650735 1,7721961 1,8856491 14 1,5125897 1,6186045 1,7316764 1,8519449 15 1,5579674 1,6753488 1,8009435 1,9352834 16 1,6017064 1,7339860 1,8729812 2,0223901 17 1,6528476 1,7946755 1,9479005 2,1133768 18 1,7024330 1,8574892 2,0258165| 2,2308478 19 1,7535060 1,9225013 2,1068492 2,3078603 20 1,8061112 1,9897888 2,1911231| 2,4117140 21 1,8602945 2,0594314 2,2787681 2,5202411 221,9161034 2,1315115 2,3699188 2,6336520 23 1,9735865 2,2061144 2,4647155 2.7521663 24 2,0327941 2,2833284 2,5633042 2.8760138 25 2,0937779 2,3632449 2,6658363 3,0054344 26 2,1565912 2,4459585 2,7724697 3,1406709 27 2,2212890 2,5315671 2,8833685 3,2820095 28 2,2879276 2,6201719 2,9987033 3,4296999 29 2,3565655 2,7118779 3,11865143,5840364 30 2,4272624 2,8067937 | 3.2433975 3,7453181 4,3219424

1,97993.6 2,0789282 2,1328746 2,2920183 2,4066192 2,5269502 2,6532977 2,7859626 2,9252607 3,0715238 3,2251000 3,3853549 3,5546527 3-7334563 3,9201291 4,1161336

Days.

TABLE

IL

The Amount of One Pound for Days.

3 per Cent. 3 per Cent.] 4per Cent. 41 per Cent. 5 per Cent.

11,0000809 1,0000942 1,0001074 1,0001206 1,0001336 21,0001619 1,0001885 1,0002149 1,2002412 1,0002973 31,0002429 1.cc02827 1,0003224 1,0003618 1,0004011 4 1,0003240 1,0003770 1,0004299 1,0004824 1,0005348

1,0004050 1,0004713 1,0005374 1,0006031 1,0006685 61,0004860 1,0005656 1,0006449 1,0007238,0008023 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 1,0018867 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,CC40573 1,0047236 | 1,c053871 | 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 90 1,0073151 1,0085 186 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 1401,0114021 1,0132825 1,0151572 1,0170265 1,0188932 150 1,0122215 1,0142379 1,0162487 1,0182537 1,0202531 160 1,0130415 1,0151943 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

When