1.0268546374 91 1.0146333511 131 8610138927895 126 1.0203184110 166 87 1.0139856501 127 1.0204813084 167 1.0270185784 88 1.0141475365 128 1.0206442319 168 1.0271825456 89 1.0143094488 129 1.0208071814 169 1.0273465389 90 1.0144713869 130 92 1.0147953408 132 1.0209701569 170 1.0275105585 93 1.0149573565 133 94 1.0151193981 134 1.0216223193 174 1.0281668989 95 1.0152814655 135 1.0217854250 175 1.0283310494 1.0164166624 142 1.0229278940 182 1.0294908372 103 1.0165789370 143 1.0230902081 183 1.0296451975 104 1.0167412375 144 1.0232545483 184 1.0298095841 105 1.0169035638 145 1.0234179146 185 1.0299739969 106 1.0170659161 146 1.0235813069 186 1.0301384359 107 1.0172282944 147 108 1.0173906985 148 1.0237447253 187 1.0303029012 1.0239081699 188 1.0304673928 109 1.0175513086 149 110 1.0177155846 150 1.0242351372 190 1.0307964557 Days Amounts of 11. Days Amounts of 17. Days Amounts of 12. &c. 196 1.0317842709 236 1.0383939484 276 1.0450459680 197 1.0319489990 237 1.0385597318 277 1.0452128133 198 1.0321137534 238 1.0387255415 278 1.0453796853 199 1.0322785341 239 1.0388913778 279 1.0455446584 200 1.0324433410 240 1.0390572405 280 1.0457135092 281 1.0458804611 282 201 1.0326081742 241 1.0392231298 202 1.0327730339 242 1.0393890454 203 1.0329379198 243 1.0395549876 283 204 1.0331028321 244 1.0397209563 284 205 1.0332677706 245 1.0398869515 285 211 1.0465484353 286 10467156206 206 1.0334327355 246 1.0400529732 207 1.0335977268 247 1.0402190214 287 1.0468827325 288 1.0470498711 208 1.0337627444 248 1.0403850961 209 1.0339277883 249 1.0405511973 289 1.0472170363 210 1.0340928586 250 1.0407173250 290 1.0473842283 1.0342579552 251 1.0408834793 291 1.0475514469 212 1.0344230782 252 1.0410496601 292 1.0477186923 213 1.0345882275 253 1.0412158674 293 1.0478859643 214 1.0347534033 254 1.0413821012 294 1.0480532631 215 1.0349186054 255 1.0415483616 295 1.0482205885 216 1.0350838338 256 1.0417146485 296 1.0483879407 217 1.0352490887 257 1.0418809620 297 1.0485553196 218 1.0354143699 258 1.0420473021 298 1.0487227252 219 1.0355796775 259 1.0422136687 299 220 221 1.0357450115 260 1.0423800618 300 301 1.0359103719 261 1.0425464815 222 1.0360757587 262 1.0427129278 302 223 1.0362411719 263 1.0428794007 303 1 0488901576 1.0490576166 1.0492251025 1.049 1.0493926150 1.0495601543 224 1.0364066116 264 1.0430459001 304 1.0497277204 225 10365710776 265 1.0432124261 305 1.0498953132 226 1.0367375701 266 1.0433789787 306 1.0500629327 227 1.0369030889 267 1.0435455579 307 1.0502305790 228 1.0370686342 268 1.0437121637 308 1.0503082521 229 1.0372342059 269 1.0438787961 309 1.0505659519 310 1.0507336786 230 1.0373998041 270 1.0440454551 231 1.0375654287 271 1.0442121407 311 1.0509014320 1.0510692121 232 1.0377310798 272 1.0443788529 312 233 1.0378967573 273 1.0445455918 313 1.0512370191 234 1.0380624612 274 1.0447123572 314 1.0514048529 235 1.0382241916 275 1.0448791493 | 315 | 1.0515727134 Days 316 1.0517406008 339 1.0556094165 362 1.0594924636 317 1.0519085150 340 1.0557779484 363 1.0596616154 318 1,0520764559 341 1.0559465071 364 1.0598307942 319 1.0522444237 342 1.0561150927 365 1.06 320 1.0524124183 343 1.0562837053 321 1.0525804397 344 1.0564523448 322 1.9527484880 345 1.0566210112 323 1.0529165631 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 328 1.0537573410 351 1.0576335753 329 1.0539255771 352 1.0578024303 330 1.0540938401 353 1.0579713122 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 3381.0554409116| 361 | 1.0593233389 Months 1 2 3 The Amounts of 1 1. at 6 per Cent. For Months. 1.0048675505 1.0097587942 1.0146738462 4 1.0196128224 5 10245758394 6 1.0295630141 7 1.0345744641 8 1.0396103076 91.0446706634 10 12 1.0497556507 1.0548653894 1.06 The Use of this Table is in all respects like that of whole Years, in finding the Amount of any given Sum for any proposed Number of Days less than a Year. 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 × 375 387,7848 &c. = 387 1. 15 s. 8d. which is the Amount required. And the rest of the Variations may be performed just as in the Examples of whole Years. But if the Time given consists 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 2. Suppose 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 Il. for 5 Years is 1,338225 &c. 1,021785 &. {135 Days is Then 1,338225 × 1,021785 × 2651. = 362,355232, &. being the Amount or Answer required. Or, if the Amount and Time are given, to find the Principal; Then Multiply the Amount of Il. 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 362l. 7 s. Id. The Amount of i for { Then 1,338225 × 1,021785 = 1,367378 &c. the Divisor. 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 Cent. &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 Interest, are given, to find the Rate of Interest; Then proceed as in the Fourth Question, Page 255, छ. Now in order to make this Table of Amounts for Days, useful for all Rates of Interest (as before in that for Years) you must first find the Simple Interest of 11. 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 : : 1 : 0,06 the Two Simple Interests 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 11. for one Day, at 6 per Cent. Their Difference 0,00005479 = x which may do indifferently well for ordinary small Questions; But where Exactness is required, it will be convenient to make Use of this Proportion. Mm Viz. 12. As the Simple Intereft of 11. for one Day at 6 per Cent: That is, 0,00016438: 0,00015965 :: 0,00021917: 0,00021286 Then 0,00021286-0,00015965=0,00005321=x. This x being involved with the respective Amounts for Days, in the fame Manner as was done with those for Years (vide Page 258) the Result will be the Anfwer to the Question. Sect. 2. Annuitics or Pensions in Arrear computed at When Annuities, &c. are faid to be in Arrear, fee Page 248. And I shall here make use of the fame Letters to represent the same Things as before in that Page, fave only that R is here equal to the Amount of 1 1. as in Section 1. of this Chapter. Suppose u = the First Year's Rent of any Annuity without Interest. Then will Ru+u= and RRu+Ru+u= { the Amount of the First Year's Rent, and its with Here RRu+Ru+u=A the Amount of any Yearly Rent or Annuity, being forborn Three Years. And from hence may be deduced these 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 Term will always be uR Confequently A- R- - the Sum of all the Antecedents Ergo Au-uu RuA-uu R' which, being divided all by u, will Lecome A-u-RA-uR. From this last Æquation it will be easy to raise the following Theorems. |