101 1.0162544138 141 1 0227646060 181 1.0293160231 149 1.0240716405 189 1.0306319206 110 112 1.0177155846 150 1.0242351372 190 1.0307964557 1.0178780665 151 1.0243986600 191 1.0309610251 1.0180405744 152 1.0245622089 192 1131.0182031083 153 1.0247257830 193 1141.0183656680 154 1.0248893851 194 1.0314548937 1.0311256216 1.0312902445 1151.0185282578155 1.0250530124 | 195 1.0316195692 Days Days 205 206 211 212 Amounts of 1l. &c. Days 276 1.0450459680 277 1.0452128133 278 1.0453796853 279 1.0455446584 280 1.0457135092 281 1.0458804611 282 1.0460474397 283 1.0462144449 1.0463814768 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 284 1.0332677706 245 1.0398869515 1.0334327355 246 1.0400529732 207 1.0335977268 247 1.0402190214 208 1.0337627444 248 1.0403850961 2091.0339277883 249 1.0405511973 210 1.0340928586 250 1.0407173250 1.0342579552 2511.0408834793 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 260 1.0423800618 220 1.0357450115 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 228 1.0370686342 268 1.0437121637 229 1.0372342059 269 1.0438787961 230 1.0373998041 270 1.0440454551 1.0442121407 231 1.0375654287 271 232 1.0377310798 272 1.0443788529 233 295 1.0482205885 1.0417146485 296 1.0483879407 297 319 1.0522444237 &c. 364 1.0594924636 1.0596616154 1.0598307942 365 1.06 Months 316 1.0517406008 339 1.0556094165 362 317 1.05 19085150 340 1.0557779484 363 318 1.0520764559 341 1.0559465071 320 1.0524124183 343 1.0562837053 342 1.0561150927 321 1.0525804397 344 1.0564523448 322 1.9527484880 345 1.0566210112 323 10529165631 346 1.0567897045 324 1.0530846650 347 1.0569584248 325 1.0532527937 348 1.0571271720 326 1.0534209493 349 1.0572959594 327 1.0535891317 350 1.0574647472 1.0537573410 351 1.0576335753 1.0539255771 330 1.0540938401 353 1.0579713122 352 1.0578024303 331 1.0542621300 354 1.0581402211 332 1.0544304467 355 1.0583091570 333 1.0545987903 356 1.0584781199 334 1.0547671608 357 1.0586471097 335 1.0549355582 358 1.0588161265 336 1.0551039824 359 1.0589851703 337 1.0552724336 360 1.0591542411 338 1.0554409116 361 1.0593233389 328 329 2 The Amounts of 1 1. at 6 per Cent. For Months. 1.0048675505 1.0097587942 1.0146738462 41.0196128224 5 I 0245758394 6 1.0295630141 7 1.0345744641 8 1.0396103076 9 1.0446706634 II 12 1.0497556507 The Use 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. Suppose it were required to find the Amount of 3751. for 210 Days at 6 per Cent. The Amount of 11. for 210 Days is 1,0340928 &c. per Table. Then 1,0340928 x 375 387,7848 &c. 387 l. 15 s. 8 d. which is the Amount required. And the rest 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 Answer 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 1 7. for 135 Days is 1,021785 &c. 5 Years is 1,338225 &c. Then 1,338225 × 1,021785 × 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 1 l. 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 362l. 7 s. 11d. Or 362,355232 l. in 5 Years and 135 Days, at 6 per Cent. &c. The Amount of i for 5 Years is 1,338225 &c. 135 Days is 1,021785 &c. Then 1,338225 X 1,021785 = 1,367378 &c. the Divifor. Next 1,367378) 362,355232 = A (255 1. the Principal required. Again, if the Principal and its Amount are given, to find the Time, at 6 per Cent. &c. you must divide the Amount by its Principal, and then proceed as in the Third Example, Page 256, for the Anfwer required. But if the Amount and its Principal, with the Time of its being at Interest, are given, to find the Rate of Intereft; Then proceed as in the Fourth Question, Page 255, &c. Now in order to make this Table of Amounts for Days, ufeful for all Rates of Intereft (as before in that for Years) you must first find the Simple Intereft of 1 l. 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 1308: 1: 0,08 And 100: 6:: I: 0,06 the Two Simple Interefts for one Year. Then 365) 0,08 (0,00021917 &c. the Simple Interest of 11. for one Day, at 8 per Cent. And 365) 0,06 (0,00016438 &c. the Simple Intereft of 1 l. for one Day, at 6 per Cent. Their Difference 0,00005479x which may do indifferently well for ordinary fmall Questions; But where Exactnefs is required, it will be convenient to make Ufe of this Proportion. Viz As the Simple Intereft of 17. for one Day at 6 per Cent: That is, 0,00016438: 0,00015965 0,00021917: 0,00021286 Then 0,00021286-0,00015965=0,00005321=x. This being involved with the refpective Amounts for Days, in the fame Manner as was done with thofe for Years (vide Page 258) the Refult will be the Anfier to the Question. Sect. 2. Annuities or Penfions 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 Inte reft. the Amount of the First Year's Rent, and its Then will Ru+u=Intereft; More the 2d Year's Rent. { and RRu+Ru+u= the Amount of the Ift 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 laft Term will always be uRt 1 I Confequently AR the Sum of all the Antecedents 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 raise the following Theorems. |