Therefore I X C 2 in Numb. 3 in Numb. 4 in Numb. 5+6+7 I\r+e=a 3 brr+2bre+bee=baa 531560+ 19449 e + 194ee560783 8-531560 9 19449+ 194ee29223_. 9194 10 100,2e+ee = 153,06 = D Or new r=41,5 for a fecond Operation, which being duly involved, &c. will be found more than juft. Therefore Then r 2 crce=ca 3 brr-2bre+bee=baa 4 rrr - 3rre+3ree=aaa These being turned into Numbers, c. as above, they will be 20037,75 € 198,5 390,375, which being divided by 198,5 the Co-efficient of, will become 100,946 e-ee= 1,966624, &c. = D. Operation 100,946 Let the laft Equation in the Enigma, Chap. 9. be here propofed for a Solution. Viz. a aaa+baaa—caa¬da=G; b = 2, c = 288, d=506, and G= 1513, Quære a. By Tryals it will be found, that the next nearest r=20, being fomething more than just. Therefore I rea Ixd 2 dr deda 2 IC хс I 3crr- zēre + cee = ca a 13x b 4 brrr—3 brre + 3b re e #ba a a I Thefe being turned into Numbers, and thofe duly collected, according as the Signs of the Equation direct, they will become 50680-22374e+ 2232ee1513, which being all divided by 2232 the Co-efficient of ee, will be 10 eee 22 — D. By what hath been already done about the Solution of these few Equations (being carefully obferved), I prefume the Learner will catily conceive how to proceed in the Solution of all Kinds of Equations, be they never fo high, or adfected; therefore I fhail not here propofe many various Examples, but only take them as they fall in Courfe, when I come to the next Part, wherein you will (perhaps) find fuch Equations with their Solutions as are not common. С НА Р. CHA P. XI. Of Simple Intereft, Annuities, or Penfions, &c. INTEREST, or the Ufe paid for the Loan of Money, is either Simple; or Compound. Sect. 1. Of Simple Intereff. SIMPLE Intereft, is that which is paid for the Loan of any Principal or Sum of Money, lent out for fome Time, at any Rate per Cent: agreed on between the Borrower and the Lender; which, according the late Laws of England, ought to be fix Pounds for the Ufe of 1001. for one Year, and twelve Pounds for the Ufe of 100l, for two Years: and fo on for a greater, or leffer Sum, proportionable to the Time propofed. There are feveral Ways of computing (or anfwering Questions. about) Simple Intereft; as by the fingle and double Rule of Three (See Page 96, &c.) others make Ufe of Tables compofed at several Rates per Cent. as Sir Samuel Moreland, in his Doctrine of Intereft, both fimple and compound, all performed by Tables; wherein he hath detected feveral material Errors committed by Sir Isaac Newton, Mr Kerfey upon Wingate, and Mr. Clavil, &c. in the Bufinefs of computing Intereft, &c. by their Tables, too tedious to be here repeated. But I fhall in this Tract take other Methods, and fhew that all Computations relating to Simple Intereft are grounded upon Arithmetick Progreffion; and from thence raise fuch general Theorems, as will fuit with all Cafes. In order to that Let Pany Principal or Sum put to Intereft. R the Ratio of the Rate, per Cent. per Annum. t=the Time of the Principal's Continuance at Interest. Viz. 100:6 :: 1:0,06 the Ratio at 6 per Cent. per Annum. And if the given Time be whole Years; then t the Number of whole Years: but if the Time be given, be either pure Parts of a Year, or Parts of a Year mixed with Years; those Parts muft be turned into Decimals; and then thofe Decimals, &c. Now Now the common Parts of a Year may be easily turned or converted into Decimal Parts, if it be confidered Thefe Things being premised, we may proceed to raifing the Theorems. = Let R the Intereft of 11. for one Year, as before. the Intereft of 1 l. for three Years. 4 Rthe Intereft of 1 1. for four Years. And, fo on for any Number of Years propofed. Hence it is plain, that the Simple Intereft of one Pound is a Series of Terms in Arithmetic Progreffion increafing; whose first Term and common Difference is R, and the Number of all the Terms is t. Therefore the laft Term will always be t R Intereft of 1 1. for any given Term fignified by t. Then the As one Pound is to the Intereft of 11. :: fe is any Then That is, I tR:: P:tRP the Intereft of P. the Principal being added to it's Intereft, their Sum will be = the Amount required: which gives this general Theorem. Theorem 1. t RP+P = A· From whence the three following Theorems are eafily deduced. Thefe four Theorems refolve all Questions about Simple Interest. Question 1. What will 2561. 10s. amount to in 3 Years, one Quarter, 2 Months, and 18 Days, at 6 per Cent. per Annum. Here is given P=256,5; R= 0,06; and 3,46599 For 3 Years 3 Quære 4. per Theorem 1. one Quarter = 0,25 2 Months 0,16667 0,08333 x 2 18 Days 0,04932 0,00274 × 18 = Hence 3,46599: × 0,06 0,2079594 R X Then 0,2079594 × 256,553,341586 RP And 53,341586 +256,5309,841586≈ RP + P = A That is, 309,841586 = 309 / 16. 10 d. being the Answer required.... Question = Question 2. What Principal or Sum being put to Interest, will raife a Stock of 309 1. 16s. 10d. in three Years, one Quarter, two Months, and 18 Days; at 6 per Cent. per Annum ? Or the fame Question otherwise stated thus. What is 3091. 16 s. 10 d. due 3 Years, one Quarter, 2 Months and 18 Days hence, worth in ready Money; abating or discounting 6 per Cent, &c. Here is given A=309,841586: R = 0,06; t = 3,46599 (found as before) thence to find P. Per Theorem 2. First 3,46599 × 0,06 = 0,2079594 = R. Then t R+1= 1,2079594) 309,841586A (256,5=P; that is, 256,5 =256, 10s. the Anfwer required. Question 3. At what Rate or Intereft, per Cent, &c. will 2561. 10s. amount to 3091. 16s. 10d. in three Years, one Quarter, two Months, and 18 Days? Here is given, P=256,5; A=309,841586; and t=3,46599 to find R. Per Theorem 3. Firft 309,841586-256,5 = 53,341586A-P. Next 3,46599 x 256,5889,026435 R. And R 889,026435) 53,341586 (00,06 = the Ratio. Then 17. : 0,06 :: 120: 6 the Rate required. = ! Question 4. In what Time will 2561. 10 s. raife a Stock of (or amount to) 309 l. 16's. 10 d. at 6 per Cent. &c. Here is given, P=256,5; A=309,841586, and R= 0,06 to find t. Per Theorem 4. First 309,841586 — 256,5 = 53,341586A-P. And 256,5 x 0,06 15,39 PR. Then 15,39) 53,341586 (3,46599; that is = 3 Years and ,46599 Decimal Parts of a Year; which may be brought into common Parts of a Year, thus 0,46599 0,21599 And 0,08333) 0,21599 (2 Months. ,16666 0,02074),04933 · (18 Days. Hence 3 Years, one Quarter, 2 Months, and 18 Days; the It muft needs be eafy to conceive, that what is here done at 6 per Cent. may be done at any other Rate of Intereft, by forming the Ratio (viz. R) accordingly. SCHOLIUM. |