1119:
720:
1179:
Businesses consider this discount rate when deciding whether to invest profits to buy equipment or whether to deliver the profit to shareholders. In an ideal world, they would buy a piece of equipment if shareholders would get a bigger profit later. The amount of extra profit a shareholder requires
1104:
thly is applied in each subinterval to a smaller (already discounted) sum of money. As such, in order to achieve the same total amount of discounting the rate has to be slightly more than 1/pth of the annual rate of discount.
1180:
to prefer that the company buy the equipment rather than giving them the profit now is based on the shareholder's discount rate. A common way of estimating shareholders' discount rates uses share price data is known as the
877:
99:
149:
998:
1040:
386:
521:
588:
473:
1208:
1081:
914:
54:
that sells for $ 95 ('balance' in the bond at the start of period) and pays $ 100 ('balance' in the bond at the end of period) in a year's time. The discount rate is
624:
657:
175:
1102:
935:
799:
700:
680:
544:
429:
409:
333:
313:
289:
269:
245:
221:
201:
1140:
741:
1209:
https://web.archive.org/web/20131230232348/http://www.mcu.edu.tw/department/management/stat/ch_web/etea/Theory%20of%20Interest/interest2.pdf
807:
44:
1166:
767:
1148:
749:
60:
110:
1144:
745:
943:
1005:
341:
1181:
482:
552:
437:
1197:
1129:
730:
1237:
1133:
734:
181:
1052:
885:
597:
633:
157:
8:
1086:
919:
783:
685:
665:
529:
414:
394:
318:
298:
274:
254:
230:
206:
186:
1185:
1043:
801:
times over equal subintervals of a year is found from the annual effective rate d as
1221:
Kellison, S. G.: The Theory of
Interest (Irwin: Illinois, 2008, 3rd edition), p.17.
51:
1231:
295:. Therefore, we have the following relationship between two equivalent rates
224:
248:
31:
of the annual period. It is related to but slightly smaller than the
1118:
719:
1184:. Businesses normally apply this discount rate by calculating the
1083:
is always bigger than d because the rate of discount convertible
104:
The effective interest rate is calculated using 95 as the base
251:
is invested for the same amount of time at each of the rates
872:{\displaystyle 1-d=\left(1-{\frac {d^{(p)}}{p}}\right)^{p}}
916:
is called the annual nominal rate of discount convertible
705:
391:
Using this, we can derive the following expression of
43:
of the period. The discount rate is commonly used for
1089:
1055:
1008:
946:
922:
888:
810:
786:
688:
668:
636:
600:
555:
532:
485:
440:
417:
397:
344:
321:
301:
277:
257:
233:
209:
189:
160:
113:
63:
23:
expresses the amount of interest paid or earned as a
203:, there is a corresponding effective discount rate
1096:
1075:
1034:
992:
929:
908:
871:
793:
694:
674:
651:
618:
582:
538:
515:
467:
423:
403:
380:
327:
307:
283:
263:
239:
215:
195:
169:
143:
93:
1229:
35:, which expresses the amount of interest as a
94:{\displaystyle {\frac {100-95}{100}}=5.00\%}
1147:. Unsourced material may be challenged and
748:. Unsourced material may be challenged and
144:{\displaystyle {\frac {100-95}{95}}=5.26\%}
1167:Learn how and when to remove this message
1090:
1056:
1009:
923:
889:
787:
768:Learn how and when to remove this message
546:as the discount factor which is given by
1108:
993:{\displaystyle 1-d=\exp(-d^{(\infty )})}
1035:{\displaystyle \,d^{(\infty )}=\delta }
1230:
662:using the above relationships between
381:{\displaystyle 1+i={\frac {1}{1-d}}.}
1145:adding citations to reliable sources
1112:
746:adding citations to reliable sources
713:
516:{\displaystyle i={\frac {d}{1-d}}.}
47:and similar financial instruments.
16:Interest as % of final balance
13:
1018:
979:
583:{\displaystyle v={\frac {1}{1+i}}}
468:{\displaystyle d={\frac {i}{1+i}}}
164:
138:
88:
14:
1249:
706:Annual discount rate convertible
1117:
718:
1215:
1068:
1062:
1021:
1015:
987:
982:
976:
965:
901:
895:
848:
842:
21:annual effective discount rate
1:
1203:
7:
1191:
1182:capital asset pricing model
223:that can produce the same
10:
1254:
1198:Notation of interest rates
291:, and they are said to be
33:effective rate of interest
1076:{\displaystyle \,d^{(p)}}
909:{\displaystyle \,d^{(p)}}
590:, then we can derive that
780:A discount rate applied
50:For example, consider a
182:effective interest rate
177:of $ 105.26 is $ 100.
1098:
1077:
1036:
994:
931:
910:
873:
795:
696:
676:
653:
620:
584:
540:
517:
469:
425:
405:
382:
329:
309:
285:
265:
241:
217:
197:
171:
145:
95:
39:of the balance at the
27:of the balance at the
1109:Business calculations
1099:
1078:
1037:
995:
932:
911:
874:
796:
697:
677:
654:
621:
619:{\displaystyle v=1-d}
585:
541:
518:
470:
426:
406:
383:
330:
310:
286:
266:
247:if a given amount of
242:
218:
198:
172:
146:
96:
1141:improve this section
1087:
1053:
1006:
944:
920:
886:
808:
784:
742:improve this section
686:
666:
652:{\displaystyle d=iv}
634:
598:
553:
530:
483:
438:
415:
395:
342:
319:
299:
275:
255:
231:
207:
187:
170:{\displaystyle 95\%}
158:
111:
61:
1097:{\displaystyle \,p}
930:{\displaystyle \,p}
794:{\displaystyle \,p}
45:U.S. Treasury bills
1094:
1073:
1032:
990:
927:
906:
869:
791:
692:
672:
649:
616:
580:
536:
526:We usually define
513:
465:
421:
401:
378:
325:
305:
281:
261:
237:
213:
193:
167:
141:
91:
1188:of the decision.
1186:net present value
1177:
1176:
1169:
1044:force of interest
856:
778:
777:
770:
695:{\displaystyle d}
675:{\displaystyle i}
578:
539:{\displaystyle v}
508:
463:
424:{\displaystyle i}
404:{\displaystyle d}
373:
328:{\displaystyle d}
308:{\displaystyle i}
284:{\displaystyle d}
264:{\displaystyle i}
240:{\displaystyle i}
216:{\displaystyle d}
196:{\displaystyle i}
130:
80:
1245:
1222:
1219:
1172:
1165:
1161:
1158:
1152:
1121:
1113:
1103:
1101:
1100:
1095:
1082:
1080:
1079:
1074:
1072:
1071:
1041:
1039:
1038:
1033:
1025:
1024:
999:
997:
996:
991:
986:
985:
936:
934:
933:
928:
915:
913:
912:
907:
905:
904:
878:
876:
875:
870:
868:
867:
862:
858:
857:
852:
851:
836:
800:
798:
797:
792:
773:
766:
762:
759:
753:
722:
714:
709:
701:
699:
698:
693:
681:
679:
678:
673:
658:
656:
655:
650:
625:
623:
622:
617:
589:
587:
586:
581:
579:
577:
563:
545:
543:
542:
537:
522:
520:
519:
514:
509:
507:
493:
474:
472:
471:
466:
464:
462:
448:
430:
428:
427:
422:
410:
408:
407:
402:
387:
385:
384:
379:
374:
372:
358:
334:
332:
331:
326:
314:
312:
311:
306:
290:
288:
287:
282:
270:
268:
267:
262:
246:
244:
243:
238:
222:
220:
219:
214:
202:
200:
199:
194:
176:
174:
173:
168:
154:which says that
150:
148:
147:
142:
131:
126:
115:
100:
98:
97:
92:
81:
76:
65:
1253:
1252:
1248:
1247:
1246:
1244:
1243:
1242:
1228:
1227:
1226:
1225:
1220:
1216:
1206:
1194:
1173:
1162:
1156:
1153:
1138:
1122:
1111:
1088:
1085:
1084:
1061:
1057:
1054:
1051:
1050:
1014:
1010:
1007:
1004:
1003:
975:
971:
945:
942:
941:
921:
918:
917:
894:
890:
887:
884:
883:
863:
841:
837:
835:
828:
824:
823:
809:
806:
805:
785:
782:
781:
774:
763:
757:
754:
739:
723:
712:
707:
687:
684:
683:
667:
664:
663:
635:
632:
631:
599:
596:
595:
567:
562:
554:
551:
550:
531:
528:
527:
497:
492:
484:
481:
480:
452:
447:
439:
436:
435:
416:
413:
412:
396:
393:
392:
362:
357:
343:
340:
339:
320:
317:
316:
300:
297:
296:
276:
273:
272:
256:
253:
252:
232:
229:
228:
208:
205:
204:
188:
185:
184:
159:
156:
155:
116:
114:
112:
109:
108:
66:
64:
62:
59:
58:
52:government bond
17:
12:
11:
5:
1251:
1241:
1240:
1238:Interest rates
1224:
1223:
1213:
1212:
1205:
1202:
1201:
1200:
1193:
1190:
1175:
1174:
1125:
1123:
1116:
1110:
1107:
1093:
1070:
1067:
1064:
1060:
1031:
1028:
1023:
1020:
1017:
1013:
1001:
1000:
989:
984:
981:
978:
974:
970:
967:
964:
961:
958:
955:
952:
949:
926:
903:
900:
897:
893:
880:
879:
866:
861:
855:
850:
847:
844:
840:
834:
831:
827:
822:
819:
816:
813:
790:
776:
775:
726:
724:
717:
711:
704:
691:
671:
660:
659:
648:
645:
642:
639:
628:
627:
615:
612:
609:
606:
603:
592:
591:
576:
573:
570:
566:
561:
558:
535:
524:
523:
512:
506:
503:
500:
496:
491:
488:
477:
476:
461:
458:
455:
451:
446:
443:
420:
400:
389:
388:
377:
371:
368:
365:
361:
356:
353:
350:
347:
324:
304:
280:
260:
236:
212:
192:
166:
163:
152:
151:
140:
137:
134:
129:
125:
122:
119:
102:
101:
90:
87:
84:
79:
75:
72:
69:
15:
9:
6:
4:
3:
2:
1250:
1239:
1236:
1235:
1233:
1218:
1214:
1211:
1210:
1199:
1196:
1195:
1189:
1187:
1183:
1171:
1168:
1160:
1150:
1146:
1142:
1136:
1135:
1131:
1126:This section
1124:
1120:
1115:
1114:
1106:
1091:
1065:
1058:
1047:
1045:
1029:
1026:
1011:
972:
968:
962:
959:
956:
953:
950:
947:
940:
939:
938:
924:
898:
891:
864:
859:
853:
845:
838:
832:
829:
825:
820:
817:
814:
811:
804:
803:
802:
788:
772:
769:
761:
751:
747:
743:
737:
736:
732:
727:This section
725:
721:
716:
715:
703:
689:
669:
646:
643:
640:
637:
630:
629:
613:
610:
607:
604:
601:
594:
593:
574:
571:
568:
564:
559:
556:
549:
548:
547:
533:
510:
504:
501:
498:
494:
489:
486:
479:
478:
459:
456:
453:
449:
444:
441:
434:
433:
432:
418:
398:
375:
369:
366:
363:
359:
354:
351:
348:
345:
338:
337:
336:
322:
302:
294:
278:
258:
250:
234:
226:
210:
190:
183:
178:
161:
135:
132:
127:
123:
120:
117:
107:
106:
105:
85:
82:
77:
73:
70:
67:
57:
56:
55:
53:
48:
46:
42:
38:
34:
30:
26:
22:
1217:
1207:
1178:
1163:
1154:
1139:Please help
1127:
1048:
1002:
881:
779:
764:
755:
740:Please help
728:
661:
525:
390:
292:
225:future value
179:
153:
103:
49:
40:
36:
32:
28:
24:
20:
18:
1204:References
293:equivalent
180:For every
37:percentage
25:percentage
1157:June 2023
1128:does not
1049:The rate
1030:δ
1019:∞
980:∞
969:−
963:
951:−
833:−
815:−
758:June 2023
729:does not
611:−
502:−
367:−
249:principal
165:%
139:%
121:−
89:%
71:−
1232:Category
1192:See also
1149:removed
1134:sources
1042:is the
750:removed
735:sources
937:thly.
882:where
626:, and
475:, and
41:start
1132:any
1130:cite
733:any
731:cite
710:thly
682:and
411:and
315:and
271:and
136:5.26
86:5.00
19:The
1143:by
960:exp
744:by
227:as
118:100
78:100
68:100
29:end
1234::
1046:.
702:.
431:.
335:.
162:95
128:95
124:95
74:95
1170:)
1164:(
1159:)
1155:(
1151:.
1137:.
1092:p
1069:)
1066:p
1063:(
1059:d
1027:=
1022:)
1016:(
1012:d
988:)
983:)
977:(
973:d
966:(
957:=
954:d
948:1
925:p
902:)
899:p
896:(
892:d
865:p
860:)
854:p
849:)
846:p
843:(
839:d
830:1
826:(
821:=
818:d
812:1
789:p
771:)
765:(
760:)
756:(
752:.
738:.
708:p
690:d
670:i
647:v
644:i
641:=
638:d
614:d
608:1
605:=
602:v
575:i
572:+
569:1
565:1
560:=
557:v
534:v
511:.
505:d
499:1
495:d
490:=
487:i
460:i
457:+
454:1
450:i
445:=
442:d
419:i
399:d
376:.
370:d
364:1
360:1
355:=
352:i
349:+
346:1
323:d
303:i
279:d
259:i
235:i
211:d
191:i
133:=
83:=
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
