782:
successive application of the interest rate applies to all of the previously accumulated amount, so instead of getting 0.05 each 6 months, one must figure out the true annual interest rate, which in this case would be 1.1025 (one would divide the 10% by two to get 5%, then apply it twice: 1.05.) This 1.1025 represents the original amount 1.00 plus 0.05 in 6 months to make a total of 1.05, and get the same rate of interest on that 1.05 for the remaining 6 months of the year. The second six-month period returns more than the first six months because the interest rate applies to the accumulated interest as well as the original amount.
331:
32:
946:= number of periods. The simplest way to understand the above formula is to cognitively split the right side of the equation into two parts, the payment amount, and the ratio of compounding over basic interest. The ratio of compounding is composed of the aforementioned effective interest rate over the basic (nominal) interest rate. This provides a ratio that increases the payment amount in terms present value.
171:
over time: $ 100 today has a different value than $ 100 in five years. This is because one can invest $ 100 today in an interest-bearing bank account or any other investment, and that money will grow/shrink due to the rate of return. Also, if $ 100 today allows the purchase of an item, it is possible
222:
It follows that if one has to choose between receiving $ 100 today and $ 100 in one year, the rational decision is to cash the $ 100 today. If the money is to be received in one year and assuming the savings account interest rate is 5%, the person has to be offered at least $ 105 in one year so that
179:
An investor who has some money has two options: to spend it right now or to invest it. The financial compensation for saving it (and not spending it) is that the money value will accrue through the interests that he will receive from a borrower (the bank account on which he has the money deposited).
781:
must be calculated first, or a more complex annuity equation must be used. Another complication is when the interest rate is applied multiple times per period. For example, suppose the 10% interest rate in the earlier example is compounded twice a year (semi-annually). Compounding means that each
210:
The operation of evaluating a present value into the future value is called capitalization (how much will $ 100 today be worth in 5 years?). The reverse operation which consists in evaluating the present value of a future amount of money is called a
933:
223:
two options are equivalent (either receiving $ 100 today or receiving $ 105 in one year). This is because if you have cash of $ 100 today and deposit in your savings account, you will have $ 105 in one year.
749:
635:
183:
Therefore, to evaluate the real worthiness of an amount of money today after a given period of time, economic agents compound the amount of money at a given interest rate. Most
429:
319:
of the initial investment): it doesn't take into account the fact that the interest earned might be compounded itself and produce further interest (which corresponds to an
286:
795:
507:
To convert an interest rate from one compounding basis to another compounding basis (between different periodic interest rates), the following formula applies:
139:
at a specific date. It measures the nominal future sum of money that a given sum of money is "worth" at a specified time in the future assuming a certain
155:. The value does not include corrections for inflation or other factors that affect the true value of money in the future. This is used in
1006:
191:
which corresponds the minimum guaranteed rate provided the bank's saving account, for example. If one wants to compare their change in
1046:
Financial analysis and decision making: tools and techniques to solve financial problems and make effective business decisions
1028:
315:
is rarely used, as compounding is considered more meaningful . Indeed, the Future Value in this case grows linearly (it's a
1087:
96:
68:
692:
466:, the interest rate for that period. Alternatively the growth rate is expressed by the interest per unit time based on
1053:
115:
75:
513:
53:
82:
1092:
49:
467:
1018:
459:
64:
380:
1002:
786:
770:
342:
769:
Problems become more complex as you account for more variables. For example, when accounting for
491:
5.91176045 % per year based on continuous compounding (simply twice the previous percentage)
679:
488:
2.95588022 % per half year based on continuous compounding (because ln 1.03 = 0.0295588022)
241:
188:
42:
928:{\displaystyle FV_{\mathrm {annuity} }={(1+r)^{n}-1 \over r}\cdot \mathrm {(payment\ amount)} }
683:
496:
478:
200:
152:
20:
1019:
Francis, Jennifer Yvonne; Stickney, Clyde P.; Weil, Roman L.; Schipper, Katherine (2010).
89:
8:
1003:
EDUCATION 2020 HOMESCHOOL CONSOLE. FORMULA FOR CALCULATING THE FUTURE VALUE OF AN ANNUITY
965:
156:
451:
320:
196:
1049:
1024:
371:
132:
192:
172:
that $ 100 will not be enough to purchase the same item in five years, because of
985:
316:
312:
232:
678:
will be 1, and to get the annual interest rate (which may be referred to as the
955:
499:), with another period as compounding basis; for the same growth rate we have:
482:
144:
1081:
960:
439:
296:
148:
140:
212:
446:
is the number of compounding periods (not necessarily an integer), and
330:
485:, the standard way of expressing the growth rate, for easy comparisons)
204:
184:
173:
168:
1021:
Financial accounting: an introduction to concepts, methods, and uses
31:
308:
495:
Also the growth rate may be expressed in a percentage per period (
470:. For example, the following all represent the same growth rate:
216:
1072:
136:
450:
is the interest rate for that period. Thus the future value
661:
is the periodic interest rate with compounding frequency
647:
is the periodic interest rate with compounding frequency
785:
This formula gives the future value (FV) of an ordinary
215:(how much $ 100 that will be received in 5 years- at a
798:
695:
516:
383:
244:
56:. Unsourced material may be challenged and removed.
1073:calculate the different FV's with one's own values
927:
744:{\displaystyle r=\left(1+{i \over n}\right)^{n}-1}
743:
629:
423:
303:is the time in years (or a fraction of year), and
280:
503:6% per year with half a year as compounding basis
1079:
1037:
1012:
1023:. South-Western Cengage Learning. p. 806.
1043:
766:the number of compounding periods per year.
630:{\displaystyle i_{2}=\left{\times }n_{2}}
116:Learn how and when to remove this message
671:If the compounding frequency is annual,
323:of the initial investment -see below-).
1080:
777:to plug into the equation. Either the
773:(annual payments), there is no simple
19:For the computer science concept, see
1048:. New York: McGraw-Hill. p. 99.
686:), the formula can be simplified to:
231:To determine future value (FV) using
361:
325:
54:adding citations to reliable sources
25:
16:Value of an asset at a specific date
13:
918:
915:
912:
909:
906:
903:
897:
894:
891:
888:
885:
882:
879:
826:
823:
820:
817:
814:
811:
808:
226:
219:, for example -are worth today?).
14:
1104:
1066:
329:
30:
41:needs additional citations for
996:
978:
921:
876:
851:
838:
789:(assuming compound interest):
424:{\displaystyle FV=PV(1+i)^{t}}
412:
399:
275:
260:
176:(increase in purchase price).
1:
971:
235:(i.e., without compounding):
462:is given by the period, and
7:
1088:Theory of value (economics)
949:
281:{\displaystyle FV=PV(1+rt)}
195:, then they should use the
162:
10:
1109:
18:
307:stands for the per annum
986:"Edgenuity for Students"
1005:Accessed: 2011-04-14. (
762:the periodic rate, and
680:effective interest rate
452:increases exponentially
189:risk-free interest rate
929:
745:
684:annual percentage rate
631:
477:6.09 % per year (
474:3 % per half year
468:continuous compounding
425:
282:
1044:Vance, David (2003).
930:
746:
632:
483:annual rate of return
479:effective annual rate
426:
283:
201:nominal interest rate
187:calculations use the
153:accumulation function
143:, or more generally,
1093:Mathematical finance
1007:Archived by WebCite®
796:
758:is the annual rate,
693:
514:
381:
242:
50:improve this article
21:Futures and promises
966:Time value of money
157:time value of money
990:auth.edgenuity.com
925:
741:
627:
421:
341:. You can help by
321:exponential growth
278:
197:real interest rate
151:multiplied by the
1030:978-0-324-65114-0
942:= interest rate;
902:
870:
722:
598:
569:
458:is positive. The
372:compound interest
362:Compound interest
359:
358:
126:
125:
118:
100:
1100:
1060:
1059:
1041:
1035:
1034:
1016:
1010:
1000:
994:
993:
982:
934:
932:
931:
926:
924:
900:
871:
866:
859:
858:
836:
831:
830:
829:
750:
748:
747:
742:
734:
733:
728:
724:
723:
715:
636:
634:
633:
628:
626:
625:
616:
611:
607:
600:
599:
597:
596:
587:
586:
577:
575:
571:
570:
568:
567:
558:
557:
548:
526:
525:
430:
428:
427:
422:
420:
419:
354:
351:
333:
326:
287:
285:
284:
279:
193:purchasing power
121:
114:
110:
107:
101:
99:
58:
34:
26:
1108:
1107:
1103:
1102:
1101:
1099:
1098:
1097:
1078:
1077:
1069:
1064:
1063:
1056:
1042:
1038:
1031:
1017:
1013:
1001:
997:
984:
983:
979:
974:
952:
875:
854:
850:
837:
835:
807:
806:
802:
797:
794:
793:
729:
714:
707:
703:
702:
694:
691:
690:
677:
667:
660:
653:
646:
621:
617:
612:
592:
588:
582:
578:
576:
563:
559:
553:
549:
547:
540:
536:
535:
534:
530:
521:
517:
515:
512:
511:
454:with time when
415:
411:
382:
379:
378:
364:
355:
349:
346:
339:needs expansion
317:linear function
313:Simple interest
243:
240:
239:
233:simple interest
229:
227:Simple interest
165:
122:
111:
105:
102:
59:
57:
47:
35:
24:
17:
12:
11:
5:
1106:
1096:
1095:
1090:
1076:
1075:
1068:
1067:External links
1065:
1062:
1061:
1054:
1036:
1029:
1011:
995:
976:
975:
973:
970:
969:
968:
963:
958:
956:Lifetime value
951:
948:
936:
935:
923:
920:
917:
914:
911:
908:
905:
899:
896:
893:
890:
887:
884:
881:
878:
874:
869:
865:
862:
857:
853:
849:
846:
843:
840:
834:
828:
825:
822:
819:
816:
813:
810:
805:
801:
752:
751:
740:
737:
732:
727:
721:
718:
713:
710:
706:
701:
698:
675:
665:
658:
651:
644:
638:
637:
624:
620:
615:
610:
606:
603:
595:
591:
585:
581:
574:
566:
562:
556:
552:
546:
543:
539:
533:
529:
524:
520:
505:
504:
493:
492:
489:
486:
475:
432:
431:
418:
414:
410:
407:
404:
401:
398:
395:
392:
389:
386:
363:
360:
357:
356:
336:
334:
299:or principal,
289:
288:
277:
274:
271:
268:
265:
262:
259:
256:
253:
250:
247:
228:
225:
164:
161:
159:calculations.
145:rate of return
124:
123:
65:"Future value"
38:
36:
29:
15:
9:
6:
4:
3:
2:
1105:
1094:
1091:
1089:
1086:
1085:
1083:
1074:
1071:
1070:
1057:
1055:0-07-140665-4
1051:
1047:
1040:
1032:
1026:
1022:
1015:
1008:
1004:
999:
991:
987:
981:
977:
967:
964:
962:
961:Present value
959:
957:
954:
953:
947:
945:
941:
872:
867:
863:
860:
855:
847:
844:
841:
832:
803:
799:
792:
791:
790:
788:
783:
780:
776:
772:
767:
765:
761:
757:
738:
735:
730:
725:
719:
716:
711:
708:
704:
699:
696:
689:
688:
687:
685:
681:
674:
669:
664:
657:
650:
643:
622:
618:
613:
608:
604:
601:
593:
589:
583:
579:
572:
564:
560:
554:
550:
544:
541:
537:
531:
527:
522:
518:
510:
509:
508:
502:
501:
500:
498:
490:
487:
484:
480:
476:
473:
472:
471:
469:
465:
461:
457:
453:
449:
445:
441:
440:present value
437:
416:
408:
405:
402:
396:
393:
390:
387:
384:
377:
376:
375:
373:
369:
366:To determine
353:
344:
340:
337:This section
335:
332:
328:
327:
324:
322:
318:
314:
310:
306:
302:
298:
297:present value
294:
272:
269:
266:
263:
257:
254:
251:
248:
245:
238:
237:
236:
234:
224:
220:
218:
214:
208:
206:
202:
198:
194:
190:
186:
181:
177:
175:
170:
160:
158:
154:
150:
149:present value
146:
142:
141:interest rate
138:
134:
130:
120:
117:
109:
98:
95:
91:
88:
84:
81:
77:
74:
70:
67: –
66:
62:
61:Find sources:
55:
51:
45:
44:
39:This article
37:
33:
28:
27:
22:
1045:
1039:
1020:
1014:
998:
989:
980:
943:
939:
937:
784:
778:
774:
768:
763:
759:
755:
753:
672:
670:
662:
655:
648:
641:
639:
506:
497:nominal rate
494:
463:
455:
447:
443:
435:
433:
368:future value
367:
365:
350:January 2010
347:
343:adding to it
338:
304:
300:
292:
290:
230:
221:
209:
182:
178:
167:Money value
166:
147:; it is the
129:Future value
128:
127:
112:
106:January 2010
103:
93:
86:
79:
72:
60:
48:Please help
43:verification
40:
460:growth rate
213:discounting
1082:Categories
972:References
169:fluctuates
76:newspapers
873:⋅
861:−
771:annuities
736:−
682:, or the
614:×
602:−
205:inflation
185:actuarial
174:inflation
950:See also
309:interest
163:Overview
787:annuity
438:is the
295:is the
217:lottery
207:rate).
131:is the
90:scholar
1052:
1027:
938:where
901:
754:where
640:where
434:where
370:using
311:rate.
291:where
203:minus
135:of an
92:
85:
78:
71:
63:
137:asset
133:value
97:JSTOR
83:books
1050:ISBN
1025:ISBN
654:and
69:news
345:.
52:by
1084::
988:.
779:PV
775:PV
668:.
481:,
442:,
436:PV
374::
293:PV
1058:.
1033:.
1009:)
992:.
944:n
940:r
922:)
919:t
916:n
913:u
910:o
907:m
904:a
898:t
895:n
892:e
889:m
886:y
883:a
880:p
877:(
868:r
864:1
856:n
852:)
848:r
845:+
842:1
839:(
833:=
827:y
824:t
821:i
818:u
815:n
812:n
809:a
804:V
800:F
764:n
760:i
756:r
739:1
731:n
726:)
720:n
717:i
712:+
709:1
705:(
700:=
697:r
676:2
673:n
666:2
663:n
659:2
656:i
652:1
649:n
645:1
642:i
623:2
619:n
609:]
605:1
594:2
590:n
584:1
580:n
573:)
565:1
561:n
555:1
551:i
545:+
542:1
538:(
532:[
528:=
523:2
519:i
464:i
456:i
448:i
444:t
417:t
413:)
409:i
406:+
403:1
400:(
397:V
394:P
391:=
388:V
385:F
352:)
348:(
305:r
301:t
276:)
273:t
270:r
267:+
264:1
261:(
258:V
255:P
252:=
249:V
246:F
199:(
119:)
113:(
108:)
104:(
94:·
87:·
80:·
73:·
46:.
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
