212 Amounts of 11. &c. Amounts of 1 l. 196 1.0317842709 236 1.0383939484 197 1.0319489990 237 1.0385597318 198 1.0321137534 238 1.0387255415 199 1.0322785341 239 1.0388913778 200 1.0324433410 240 1.0390572405 2011.0326081742 241 1.0392231298 202 1.0327730339 242 1.0393890454 203 1.0329379198 243 1.0395549876 204 1.0331028321 244 1.0397209563 205 1.0332677706 245 1.0398869515 206 1.0334327355 246 1.04005 29732 207 1.0335977268 247 1.0402190214 208 1.0337627444 248 1.0403850961 249 1.0405511973 209 1.0339277883 210 1.0340928586 250 1.0407173250 2111.0342579552 251 1.0408834793 1.0344230782 252 1.0410496601 213 1.0345882275 253 1.0412158674 214 1.0347534033 254 1.0413821012 215 1.0349186054 255 1.0415483616 216 1.0350838338 256 1.0417146485 217 1.0352490887. 257 1.0418809620 218 1.0354143699 258 1.0420473021 219 1.0355796775 259 1.0422136687 1.0357450115 260 1.0423800618 261 1.0425464815 221 1.0359103719 222 1.0360757587 262 1.0427129278 223 1.0362411719 263 1.0428794007 224 1.0364066116 264 1.0430459001 225 1.0365710776 265 1.0432124261 226 1.0367375701 266 1.0433789787 227 1.0369030889 267 1.0435455579 268 1.0437121637 228 1.0370686342 268 229 1.0372342059 269 1.0438787961 230 1.0373998041 270 1.0440454551 231 1.0375654287 271 1.0442121407 232 1.0377310798 272 1.0443788529 233 1.0378967573 273 1.0445455918 234 1.0380624612 274 1.0447123572 235 1.0382241916 275 1.0448791493 220 1.0417146485 Amounts of Il. &c. 276 1.0450459680 277 1.0452128133 278 1.0453796853 279 1.0455446584 280 1.0457135092 281 1.0458804611 282 1.0460474397 283 1.0462144449 284 1.0463814768 285 I 0465484353 286 1 0467156205 287 1.0468827325 288 1.0470498711 289 1.0472170363 290 1.0473842283 291 1.0475514469 292 1.0477186923 293 1.0478859643 294 1.0480532631 295 1.0482205885 296 296 1.0483879407 297 1.0485553196 1.0487227252 299 1 0488901576 1.0490576166 298 303 1.0495601543 304 1.0497277204 305 1.0498953133 306 1.0500629327 307 1.0502305790 1.0503082521 308 309 309 1.0505659519 310 1.0507336786 311 1.0509014320 372 1.0510692121 313 314 315 1.05123701911.0514048529 1.0515727134 . Days Days Amounts of 1l. &c. 364 1.0594924636 1.0596616154 1.0598307942 Months 1 316 1.0517406008 339 1.0556094165 23+ 3 1.06 For Months. 1.0048675505 1.0097587942 1.0146738462 41.0196128224 5 1 0245758394 61.0295630141 1.0345744641 1.0396103076 9 1.0446706634 1.0497556507 1.0548653894 78 1.06 The Ufe of this Table is in all refpects like that of whole Years, in finding the Amount of any given Sum for any propofed Number of Days lefs than a Year. EXAMPLE 1. Suppofe it were required to find the Amount of 3751. for 210 Days at 6 per Cent. The Amount of 17. for 210 Days is 1,0340928 &c. per Table. Then 1,0340928 x 375 387,7848 &c. 387 l. 15 s. 8 4 d. which is the Amount required. And the reft of the Variations may be performed juft as in the Examples of whole Years. But if the Time given confifts of Years, and Parts of a Year; as Quarters, Months, &c. Then reduce the odd Time or Parts of the Year into Days; and the Anfwer may then be found at two Operations; as in the following Example. EXAMPLE : Example 2. Suppofe it were required to find what 2651. would amount to in five Years and 135 Days at 6 per Cent. &c. First the Amount of 11. for 135 Days is 1,021785 & S 5 Years is 1,338225 &c. Then 1,338225 X 1,021785 X 2651.362,355232, &c. being the Amount or Anfwer required. Or, if the Amount and Time are given, to find the Principal; Then Multiply the Amount of 11. for the Years, and the Amount of 11. for the odd Days together; And by their Product divide the given Amount, the Quotient will be the Principal required. Example 3. What Principal will raise a Stock of 3621. 7 s. 1d. Or 362,355232 l. in 5 Years and 135 Days, at 6 per Cent. &c. The Amount of 1 for 5 Years is 1,338225 &c. 135 Days is 1,021785 &c. Then 1,338225 × 1,021785 = 1,367378 &c. the Divifor. Next 1,367378) 362,355232 = A (265 1. the Principal required. Again, if the Principal and its Amount are given, to find the Time, at 6 per Gent. &c. you must divide the Amount by its Principal, and then proceed as in the Third Example, Page 256, for the Answer required. But if the Amount and its Principal, with the Time of its being at Intereft, are given, to find the Rate of Intereft; Then proceed as in the Fourth Queftion, Page 255, &c. Now in order to make this Table of Amounts for Days, useful for all Rates of Intereft (as before in that for Years) you must first find the Simple Intereft of 1 1. for one Day, both at the given Rate, and alfo at 6 per Cent. And call their Difference x. Thus, fuppofe the given Ratio were 8 per Cent. per Annum. First 130:8 1: 0,08 And 100: 6: : : 0,06 the Two Simple Interefts for one Year. Then 365) 0,08 (0,00021917 &c. the Simple Intereft of 11. for one Day, at 8 per Cent: And 365) 0,06 (0,00016438 &c. the Simple Interest of 11. for one Day, at 6 per Cent. Their Difference 0,00005479x which may do indifferently well for ordinary fmall Questions; But where Exactness is required, it will be convenient to make Ufe of this Proportion. M m Viz. Viz. As the Simple Intereft of 11. for one Day at 6 per Cent: That is, 0,00016438: 0,00015965 :: 0,00021917: 0,00021286 Then 0,00021285-0,00015965 0,00005321=x. This being involved with the respective Amounts for Days, in the fame Manner as was done with those for Years (vide Page 258) the Refult will be the Answer to the Question. Set. 2. Annuities or Pentions in Arrear computed at When Annuities, &c. are faid to be in Arrear, fee Page 248. And I fhall here make use of the fame Letters to represent the fame Things as before in that Page, fave only that R is here equal to the Amount of 1 l. as in Section 1. of this Chapter. Suppofe u the First Year's Rent of any Annuity without Intereft. S the Amount of the First Year's Rent, and its Then will Ru+u={Interest; More the 2d Year's Rent. and RRu+Ru+u= the Amount of the 1st and 2d Years Rents, with their Interefts; More the 3d Year's Rent, &c. Here RRu+ Ru+u-A the Amount of any Yearly Rent or Annuity, being forborn Three Years. And from hence may be deduced thefe Proportions. Viz. u: Ru:: Ru: RRu:: RRu: RRRu and fo on in for any Number of Terms or Years denoted by t, wherein the last Tera will always be uRt 1 I Confequently A-u R-- the Sum of all the Antecedents And A-u-the Sum of all the Confequents in the Series. And therefore it would be u: uR:: A-uR: A-u Vide Page 188. Ergo Au-uu Ru A-uu R' which, being divided all by u, will become A-u=RA-uR. From this laft Equation it will be eafy to raife the following Theorems. Theorem 3. { RA+U-A R. If this Equation be continually divided by R, until nothing remain, the Number of thofe Divi fions will be t. See Page 255. A Theorem 4. {R-R A-u into Numbers, according to the Method propofed in Sect. 3. Chap. 10. the Root will fhew the Value of R. Question 1. If 301. Yearly Rent, or Annuity, &c. be forborn (i. e. remain unpaid) Nine Years; what will it amount to, at 6 per Cent. per Annum Compound Interest? Here is given u=30, t=9, and R1,06; to find A. per Theorem I. R=1,689479 By the Table of Amounts for Years 30=u Ru=50,684370 —4=30, R-1=0,06) 20,684370 (344,7395=3441. 14s. 9id.—A the Amount required. Question 2. What Yearly Rent or Annuity, &c. being for born or unpaid Nine Years, will raise a Stock of 3447. 14s. 9 d. 344,7395, at 6 per Cent. &c. Here is given A=344,7395, t=9, and R1,06; to find per Theorem 2. AR=344,7395X1,06=365,42387 -1=344,7395 R'—1=1,689479-1=0,689479) 20,68437 (30=u Question 3. In what Time will 30l. Yearly Rent raise a Stock or Amount to 344. 14s. 9id. allowing 6 per Cent. for the Forbearance of Payments? Here is given u=30, A=344,7395, and R-1,06; to find t. per Theorem 3. First AR+u-A=365,42387+30--344,7395=50,68437• And u=30) 50,68437 (1,689479=R'. Then R=1,06) 1,689479 (1,593848. And 1,06) 1,593848 (1,50363; and fo on until it become 1,06) 1,06 (1. which will be at the Ninth Divifion; therefore t=9. M m 2 Or |