(57) What is the present worth of 1000/ due at 5 Months, at 44 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 144/ 11s 63d now for a Sun 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 9817 10s 5d. what was the Sum first due ? (61) A Person paid 9111/ 3s 84d for a Debt due 10 Months hence, he being allowed 4 per Cent. for the Discount. How much was the Debt? Gase 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 144/ 12s 62d 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 981/ 10s 5d for 100/ due at a certain Time to come, allowing 4 per Cent. Discount. I desire to know in what Time the Debt should have been discharged without any Rebate? (64) I have received 9111/ 3s 8d 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 Monthshence, produce 144/ 11s 64d. for the present Pay ment? (66) At what Rate per Cent. will 1000l. payable at 5 Months hence, produce 981/ 10s 5d. for the present Payment? (67) At what Rate per Cent. will 93421. payable 10 Months hence, produce 9111/ 3s 8d. for the present Pay ment ? 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 respective Time. of each Payment for its Thus, THEOREM 23. P. tr+1 2. Add all the present Worths together, and call that Sum P; then will s-p=D, the Rebate. d 3. And pr =E, the true equated Time. EXAMPLES. (68) Bowes C 14007. which was to have been paid as fol lows: 400/ down; 500/ 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 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 12/ 6s of Use 47 Days, at any Rate of Interest? (70) Put out 3841. to Interest, and in 84 Years there were 542/ 8s. found to be due. What Rate of Interest could then be implied? As. { LXVII. COMPOUND INTEREST. The Letters made use of here are A, the Amount. P, the Principal. T, the Time. R, the Amount of 17. for 1 Year, at any given Rate, which is found by the following Proportion. Thus, 100: 105 :: 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, shwoing 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=1,1025. Also, 1,05 × 1,05 × 1,05—1,157625the 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 1. for a Day; the Amount of 1 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 × 1,0001336 × 1,0001336=1,0004011, the Amount of 17. at 5 per Cent, for 3 Days, Compound Interest. TABLE I. The Amount of One Pound for Years. ears. 3 per Cent. 3per Cent. 4 per Cent. 4 percent. 5 per Cent. 61.1948523 7 1.2298733 1.2722792 1.3159318 I 1.0300000 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 1.2292553 1.2653190 1.3022601 I.34009: 6 1.3608618 1.4071004 8 1.2667700 1.3168090 1.3685691 1.4221006 1.4744554 9 1.3047731 1.3628973 1.4223118 1.4860251 1.5513282 1.3439163 1.4105987 1.4862443 15529694 1.6288946 | 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 1.9352834 2.0789282 15 1.5579674 1.6753488 1.8009435 16 1.6017064 1.7339860 1.8729812 2.0223901 2.1828746 17, 1.6528476 1.7946755 1.9479005 2.1133768 2.2920183 18 1.70243301.8574892 2.0258165 2.2308478 2.4066192 19 1.7535060 1.9225013 2.1068492 | 2.3978603 | 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 |