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CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIICATI!N TA"LE #"$ T!PIC% ")ief E*e)ci'e '
E*e)ci'e'
To&ic'
(ue'tion'
,-
P)e'ent .a .alue conce&t'-
,/ 0/ 1/ 2/ 3/ 4/ ,5/ ,4
0 0-
'e of ta+le'-
,1/ ,2
7
,
1-
P)e'ent an and fu futu) tu)e .alue &)o+lem'8 a- n9no:n futu)e amount-
5/ ,4
,/ 3/ ,1
0/ 1/ 2/ 6
+- n9no:n &ayment'-
,;/ ,,/ ,0
6/ ,0/ ,5
7/ ,6/ ,5
0/ 5
2/ 4
,;/ ,3
0
c- n9no:n num+e) of &e)iod'-
P)o+lem'
d- n9no:n inte)e't )ate-
,3/ ,7
1/ ,,/ ,6
4/ ,;/ ,,
0/ 5
e- n9no:n &)e'ent .alue-
7/ ,4
0/ 5/ 7/ ,;/ ,2
1/ 2/ 3/ 6/ 7/ ,0/ ,5/ ,7/ ,4
,/ 2/ 6/ 5/ 4/ ,1/ ,2/ ,3
2-
Value lue of of a 'e)ie e)ie' ' of i))egula) de&o'it'< changing inte)e't )ate'-
1/ 3/ 7
3 3-
Valuat luatio ion n of of lea lea'e 'e' '/ &en'ion'/ +ond'< choice +et:een &)o=ect'-
6
6 6-
>efe))ed annuity-
,6
5 5-
E*&ected ca'h flo:'-
,3
5/ ,0/ ,1/ ,2/ ,3
,/ 1/ 3/ 6/ 7/ 4/ ,;/ ,,/ ,0
0;/ 0,/ 00
,1/ ,2/ ,3
Co&y Co&y)ig )ight ht ? 0;, 0;,, @oh @ohn n ile iley y B Son'/ Son'/ Inc Inc-- ie'o ie'o// Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 6,
ASSIGNMENT CLAS C LASSIICAT SIICATI!N I!N TA"LE TA"LE #"$ LEARNING !"@ECTIVE% Lea)ning !+=ecti.e'
")ief E*e)ci'e'
E*e)ci'e'
P)o+lem'
,- Identi Identify fy accoun accountin ting g to&i to&ic' c' :he)e :he)e the time .alue of money i' )ele.ant0- >i't >i'tin ingu gui' i'h h +et:e +et:een en 'im& 'im&le le and and com&ound inte)e't-
0
1- 'e 'e a&&)o a&&)o&)i &)iat ate e com&o com&oun und d inte)e inte)e't 't ta+le'-
,
2- Identi Identify fy .a)ia+ .a)ia+le' le' fundame fundamenta ntall to to 'ol.ing inte)e't &)o+lem'3- Sol. Sol.e e futu)e futu)e and &)e'en &)e'entt .alu .alue e of of , &)o+lem'-
,/ 0/ 1/ 2/ 5/ 7
0/ 1/ 6/ 4/ ,;/ ,3
,/ 0/ 1/ 3/ 5/ 4/ ,;
6- Sol. Sol.e e futu)e futu)e .alue .alue of o)dina o)dina)y )y and and annuity due &)o+lem'-
3/ 6/ 4/ ,1
1/ 2/ 3/ 6/ ,3/ ,6
0/ 5/ ,;
5-
,;/ ,,/ ,0/ ,2/ ,6/ ,5
1/ 2/ 3/ 6/ ,,/ ,0/ ,5/ ,7/ ,4
,/ 1/ 2/ 3/ 5/ 7/ 4/ ,;/ ,1/ ,2
,3
3/ 5/ 7/ ,1/ ,2
6/ ,,/ ,0
0;/ 0,/ 00
,1/ ,2/ ,3
Sol. Sol.e e &)e' &)e'ent ent .alue .alue of o)di o)dina)y na)y and annuity due &)o+lem'-
7- Sol. Sol.e e &)e'e &)e'ent nt .al .alue ue &)o+ &)o+lem lem' ' )elat )elated ed to defe))ed annuitie' and +ond'4- A&&ly A&&ly e*&ec e*&ected ted ca'h ca'h flo:' flo:' to &)e'ent .alue mea'u)ement-
60 Co&y)i Co&y)ight ght ? 0;, 0;,, , @oh @ohn n ile iley y B Son'/ Son'/ Inc Inc-- ie'o ie'o// Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
ASSIGNMENT CHARACTERISTICS TA"LE
Item
>e'c)i&tion
E6, E60 E61
'ing inte)e't ta+le'Sim&le and com&ound inte)e't com&utation'Com&utation of fut futu)e .alue' and &)e'ent .alue'Com&utation of fut futu)e .alue' and &)e'ent .alue'Com&utation of &)e'ent .alueutu)e .alue and &)e'ent .alue &)o+lem'Com&utation of +ond &)ice'Com&utation' fo) a )eti)ement fundn9no:n )aten9no:n &e)iod' and un9no:n inte)e't )ateE.aluation of &u)cha'e o&tion'Analy'i' of alte)nati.e'Com&utation of +ond lia+ilityCom&utation of &en'ion lia+ilityIn.e'tment deci'ionReti)ement of de+tCom&utation of amount of )ental'Lea't co'tly &ayoffLea't co'tly &ayoffE*&ected ca'h flo:'E*&ected ca'h flo:' and &)e'ent .alueai) .alue e'timate-
E62 E63 E66 E65 E67 E64 E6,; E6,, E6,0 E6,1 E6,2 E6,3 E6,6 E6,5 E6,7 E6,4 E60; E60, E600 P6, P60 P61 P62 P63 P66 P65 P67 P64 P6,; P6,, P6,0 P6,1 P6,2 P6,3
Va)iou' time .alue 'ituation'Va)iou' time .alue 'ituation'Analy'i' of alte)nati.e'E.aluating &ayment alte)nati.e'Analy'i' of alte)nati.e'Pu)cha'e &)ice of a +u'ine''Time .alue conce&t' a&&lied to 'ol.e +u'ine'' &)o+lem'Analy'i' of alte)nati.e'Analy'i' of +u'ine'' &)o+lem'Analy'i' of lea'e .'- &u)cha'ePen'ion fundingPen'ion fundingE*&ected ca'h flo:' and &)e'ent .alueE*&ected ca'h flo:' and &)e'ent .alueai) .alue e'timate-
Le.el of >ifficulty
Time #minute'%
Sim&le Sim&le Sim&le
3F,; 3F,; ,;F,3
Mode)ate
,3F0;
Sim&le Mode)ate Mode)ate Sim&le Mode)ate Sim&le Mode)ate Sim&le Mode)ate Mode)ate Mode)ate Sim&le Sim&le Sim&le Sim&le Sim&le Mode)ate Mode)ate
,;F,3 ,3F0; ,0F,5 ,;F,3 3F,; ,;F,3 ,;F,3 ,;F,3 ,3F0; ,3F0; ,3F0; ,;F,3 ,;F,3 ,;F,3 ,;F,3 3F,; ,3F0; ,3F0;
Mode)ate Mode)ate Mode)ate Mode)ate Mode)ate Mode)ate Com&le*
,3F0; ,3F0; 0;F1; 0;F1; 0;F03 03F1; 1;F13
Mode)ate Com&le* Com&le* Com&le* Mode)ate Mode)ate Mode)ate Com&le*
0;F1; 1;F13 1;F13 03F1; 0;F03 0;F03 0;F03 0;F03
Co&y Co&y)ig )ight ht ? 0;, 0;,, @oh @ohn n ile iley y B Son'/ Son'/ Inc Inc-- ie'o ie'o// Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 61
LEARNING !"@ECTIVES !"@ECTIVES ,01236574-
Identify Identify accounti accounting ng to&ic' to&ic' :he)e the the time .alu .alue e of money i' i' )ele.ant )ele.ant->i'tingui >i'tingui'h 'h +et:e +et:een en 'im&le 'im&le and and com&ound com&ound inte) inte)e'te't'e a&&)o& a&&)o&)ia )iate te com&oun com&ound d inte)e' inte)e'tt ta+le'ta+le'Identify Identify .a)ia+ .a)ia+le' le' fundamenta fundamentall to 'ol.ing 'ol.ing inte)e't inte)e't &)o+le &)o+lem'm'Sol.e Sol.e futu)e futu)e and and &)e'ent &)e'ent .alue .alue of , &)o+lem &)o+lem''Sol.e Sol.e futu)e futu)e .alu .alue e of o)dina) o)dina)y y and annuity annuity due due &)o+lem &)o+lem''Sol.e Sol.e &)e'ent &)e'ent .alue .alue of o)dina)y o)dina)y and annuity annuity due &)o+lem' &)o+lem'-Sol.e Sol.e &)e'ent &)e'ent .alue .alue &)o+lem' &)o+lem' )elated )elated to defe)) defe))ed ed annuitie' annuitie' and +ond'+ond'A&&ly A&&ly e*&ect e*&ected ed ca'h flo:' flo:' to &)e'e &)e'ent nt .alue .alue mea'u)em mea'u)ementent-
62 Co&y)i Co&y)ight ght ? 0;, 0;,, , @oh @ohn n ile iley y B Son'/ Son'/ Inc Inc-- ie'o ie'o// Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
CHAPTER REVIE ,- #S-!- ,% Cha&te) 6 di'cu''e' the e''ential' of com&ound inte)e't/ annuitie' and &)e'ent .alue- The'e techniue' a)e +eing u'ed in many a)ea' of financial )e&o)ting :he)e the )elati.e .alue' of ca'h inflo:' and outflo:' a)e mea'u)ed and analyed- The mate)ial &)e'ented in Cha&te) 6 :ill &)o.ide a 'ufficient +ac9g)ound fo) a&&lication of the'e techniue' to to&ic' &)e'ented in 'u+'euent cha&te)'0- Com&ound inte)e't/ annuity/ and &)e'ent .alue techniue' can +e a&&lied to many of the item' found in financial 'tatement'- In accounting/ the'e techniue' can +e u'ed to mea'u)e the )elati.e .alue' of ca'h inflo:' and outflo:'/ e.aluate alte)nati.e in.e'tment o&&o)tunitie'/ and dete)mine &e)iodic &ayment' nece''a)y to meet futu)e o+ligation'- Some of the accounting item' to :hich the'e techniue' may +e a&&lied a)e8 #a% note' )ecei.a+le and &aya+le/ #+% lea'e'/ #c% &en'ion'/ #d% longte)m a''et'/ #e% 'in9ing fund'/ #f% +u'ine'' com+ination'/ #g% di'clo'u)e'/ and #h% in'tallment cont)act'Natu)e of Inte)e't 1- #S-!- 0% Inte)e't i' the &ayment fo) the u'e of money- It i' no)mally 'tated a' a &e)centage of the amount +o))o:ed #&)inci&al%/ calculated on a yea)ly +a'i'- o) e*am&le/ an entity may +o))o: 3/;;; f)om a +an9 at 5J inte)e't- The yea)ly inte)e't on thi' loan i' 13;- If the loan i' )e&aid in 'i* month'/ the inte)e't due :ould +e ,K0 of 13;/ o) ,53- Thi' ty&e of inte)e't com&utation i' 9no:n a' 'im&le inte)e't +ecau'e the inte)e't i' com&uted on the amount of the &)inci&al only- The fo)mula fo) 'im&le inte)e't can +e e*&)e''ed a' & i n :he)e & i' the &)inci&al/ i i' the )ate of inte)e't fo) one &e)iod/ and n i' the num+e) of &e)iod'Com&ound Inte)e't 2- #S-!- 0% Com&ound inte)e't i' the &)oce'' of com&uting inte)e't on the &)inci&al &lu' any inte)e't &)e.iou'ly ea)ned- Refe))ing to the e*am&le in #1% a+o.e/ if the loan :a' fo) t:o yea)' :ith inte)e't com&ounded annually/ the 'econd yea)D' inte)e't :ould +e 152-3; #&)inci&al &lu' fi)'t yea)D' inte)e't multi&lied +y 5J%- Com&ound inte)e't i' mo't common in +u'ine'' 'ituation' :he)e la)ge amount' of ca&ital a)e financed o.e) long &e)iod' of time- Sim&le inte)e't i' a&&lied mainly to 'ho)tte)m in.e'tment' and de+t' due in one yea) o) le''- Ho: often inte)e't i' com&ounded can ma9e a 'u+'tantial diffe)ence in the le.el of )etu)n achie.ed3- In di'cu''ing com&ound inte)e't/ the te)m &e)iod i' u'ed in &lace of yea)' +ecau'e inte)e't may +e com&ounded daily/ :ee9ly/ monthly/ and 'o on- Thu'/ to con.e)t the annual inte)e't )ate to the com&ounding Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 63
&e)iod inte)e't )ate/ di.ide the annual inte)e't )ate +y the num+e) of com&ounding &e)iod' in a yea)- Al'o/ the num+e) of &e)iod' o.e) :hich inte)e't :ill +e com&ounded i' calculated +y multi&lying the num+e) of yea)' in.ol.ed +y the num+e) of com&ounding &e)iod' in a yea)-
66 Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
Time Value of Money Ta+le' 6- #S-!- 1% Com&ound inte)e't ta+le' ha.e +een de.elo&ed to aid in the com&utation of &)e'ent .alue' and annuitie'- Ca)eful analy'i' of the &)o+lem a' to :hich com&ound inte)e't ta+le' :ill +e a&&lied i' nece''a)y to dete)mine the a&&)o&)iate &)ocedu)e' to follo:5- The follo:ing i' a 'umma)y of the content' of the fi.e ty&e' of com&ound inte)e't ta+le'8 utu)e .alue of , ta+le- Contain' the amount' to :hich , :ill accumulate if de&o'ited no: at a '&ecified )ate and left fo) a '&ecified num+e) of &e)iod'- #Ta+le ,% P)e'ent .alue of , ta+le- Contain' the amount' that mu't +e de&o'ited no: at a '&ecified )ate of inte)e't to eual , at the end of a '&ecified num+e) of &e)iod'- #Ta+le 0% utu)e .alue of an o)dina)y annuity of , ta+le- Contain' the amount' to :hich &e)iodic )ent' of , :ill accumulate if the &ayment' #)ent'% a)e in.e'ted at the end of each &e)iod at a '&ecified )ate of inte)e't fo) a '&ecified num+e) of &e)iod'- #Thi' ta+le may al'o +e u'ed a' a +a'i' fo) con.e)ting to the amount of an annuity due of ,-% #Ta+le 1% P)e'ent .alue of an o)dina)y annuity of , ta+le- Contain' the amount' that mu't +e de&o'ited no: at a '&ecified )ate of inte)e't to &e)mit :ithd)a:al' of , at the end of )egula) &e)iodic inte).al' fo) the '&ecified num+e) of &e)iod'- #Ta+le 2% P)e'ent .alue of an annuity due of , ta+le- Contain' the amount' that mu't +e de&o'ited no: at a '&ecified )ate of inte)e't to &e)mit :ithd)a:al' of , at the +eginning of )egula) &e)iodic inte).al' fo) the '&ecified num+e) of &e)iod'- #Ta+le 3% 7- #S-!- 2% Ce)tain conce&t' a)e fundamental to all com&ound inte)e't &)o+lem'- The'e conce&t' a)e8 a- Rate of Inte)e't- The annual )ate that mu't +e ad=u'ted to )eflect the length of the com&ounding &e)iod if le'' than a yea)+- Num+e) of Time Pe)iod'- The num+e) of com&ounding &e)iod' #a &e)iod may +e eual to o) le'' than a yea)%c- utu)e Amount- The .alue at a futu)e date of a gi.en 'um o) 'um' in.e'ted a''uming com&ound inte)e'td- P)e'ent Value- The .alue no: #&)e'ent time% of a futu)e 'um o) 'um' di'counted a''uming com&ound inte)e'tCo&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 65
4- #S-!- 3% The )emaining )e.ie: &a)ag)a&h' &e)tain to &)e'ent .alue' and futu)e .alue'- The te*t mate)ial co.e)' the follo:ing 'i* ma=o) time .alue of money conce&t'8 a- utu)e .alue of a 'ingle 'um+- P)e'ent .alue of a 'ingle 'umc- utu)e .alue of an o)dina)y annuityd- utu)e .alue of an annuity duee- P)e'ent .alue of an o)dina)y annuityf- P)e'ent .alue of an annuity due,;- Single'um &)o+lem' gene)ally fall into one of t:o catego)ie'- The fi)'t catego)y con'i't' of &)o+lem' that )eui)e the com&utation of the un9no:n futu)e .alue of a 9no:n 'ingle 'um of money that i' in.e'ted no: fo) a ce)tain num+e) of &e)iod' at a ce)tain inte)e't )ate- The 'econd catego)y con'i't' of &)o+lem' that )eui)e the com&utation of the un9no:n &)e'ent .alue of a 9no:n 'ingle 'um of money in the futu)e that i' di'counted fo) a ce)tain num+e) of &e)iod' at a ce)tain inte)e't )ateP)e'ent Value ,,- The conce&t of &)e'ent .alue i' de'c)i+ed a' the amount that mu't +e in.e'ted no: to &)oduce a 9no:n futu)e .alue- Thi' i' the o&&o'ite of the com&ound inte)e't di'cu''ion in :hich the &)e'ent .alue :a' 9no:n and the futu)e .alue :a' dete)mined- An e*am&le of the ty&e of ue'tion add)e''ed +y the &)e'ent .alue method i'8 hat amount mu't +e in.e'ted today at 6J inte)e't com&ounded annually to accumulate 3/;;; at the end of ,; yea)'O In thi' ue'tion the &)e'ent .alue method i' u'ed to dete)mine the initial dolla) amount to +e in.e'ted- The &)e'ent .alue method can al'o +e u'ed to dete)mine the num+e) of yea)' o) the inte)e't )ate :hen the othe) fact' a)e 9no:nutu)e Value of an Annuity ,0- #S-!- 6% An annuity i' a 'e)ie' of eual &e)iodic &ayment' o) )ecei&t' called )ent'- An annuity )eui)e' that the )ent' +e &aid o) )ecei.ed at eual time inte).al'/ and that com&ound inte)e't +e a&&lied- The futu)e .alue of an annuity i' the 'um #futu)e .alue% of all the )ent' #&ayment' o) )ecei&t'% &lu' the accumulated com&ound inte)e't on them- If the )ent' occu) at the end of each time &e)iod/ the annuity i' 9no:n a' an o)dina)y annuity- If )ent' occu) at the +eginning of each time &e)iod/ it 67 Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
i' an annuity due- Thu'/ in dete)mining the amount of an annuity fo) a gi.en 'et of fact'/ the)e :ill +e one le'' inte)e't &e)iod fo) an o)dina)y annuity than fo) an annuity dueP)e'ent Value of an Annuity ,1- #S-!- 5% The &)e'ent .alue of an annuity i' the 'ingle 'um that/ if in.e'ted at com&ound inte)e't no:/ :ould &)o.ide fo) a 'e)ie' of eual :ithd)a:al' fo) a ce)tain num+e) of futu)e &e)iod'- If the annuity i' an o)dina)y annuity/ the initial 'um of money i' in.e'ted at the +eginning of the fi)'t &e)iod and :ithd)a:al' a)e made at the end of each &e)iod- If the annuity i' an annuity due/ the initial 'um of money i' in.e'ted at the +eginning of the fi)'t &e)iod and :ithd)a:al' a)e made at the +eginning of each &e)iod- Thu'/ the fi)'t )ent :ithd)a:n in an annuity due occu)' on the day afte) the initial 'um of money i' in.e'tedhen com&uting the &)e'ent .alue of an annuity/ fo) a gi.en 'et of fact'/ the)e :ill +e one le'' di'count &e)iod fo) an annuity due than fo) an o)dina)y annuity>efe))ed Annuitie' ,2- #S-!- 7% A defe))ed annuity i' an annuity in :hich t:o o) mo)e &e)iod' ha.e e*&i)ed +efo)e the )ent' :ill +egin- o) e*am&le/ an o)dina)y annuity of ,; annual )ent' defe))ed fi.e yea)' mean' that no )ent' :ill occu) du)ing the fi)'t fi.e yea)'/ and that the fi)'t of the ,; )ent' :ill occu) at the end of the 'i*th yea)- An annuity due of ,; annual )ent' defe))ed fi.e yea)' mean' that no )ent' :ill occu) du)ing the fi)'t fi.e yea)'/ and that the fi)'t of the ,; )ent' :ill occu) at the +eginning of the 'i*th yea)- The fact that an annuity i' a defe))ed annuity affect' the com&utation of the &)e'ent .alue- Ho:e.e)/ the futu)e .alue of a defe))ed annuity i' the 'ame a' the futu)e .alue of an annuity not defe))ed +ecau'e the)e i' no accumulation o) in.e'tment on :hich inte)e't may acc)ue,3- A longte)m +ond &)oduce' t:o ca'h flo:'8 #,% &e)iodic inte)e't &ayment' du)ing the life of the +ond/ and #0% the &)inci&al #face .alue% &aid at matu)ity- At the date of i''ue/ +ond +uye)' dete)mine the &)e'ent .alue of the'e t:o ca'h flo:' u'ing the ma)9et )ate of inte)e't,6- #S-!- 4% Inte)national Accounting Standa)d No- 6 int)oduce' an e*&ected ca'h flo: a&&)oach that u'e' a )ange of ca'h flo:' and inco)&o)ate' the &)o+a+ilitie' of tho'e ca'h flo:' to &)o.ide a mo)e )ele.ant mea'u)ement of &)e'ent .alue- The IAS" ta9e' the &o'ition that afte) com&uting the e*&ected ca'h flo:'/ a com&any 'hould di'count tho'e ca'h flo:' +y the )i'9f)ee )ate of )etu)n/ :hich i' defined a' the &u)e )ate of )etu)n &lu' the e*&ected inflation )ate-
Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 64
LECTRE !TLINE Thi' cha&te) can +e co.e)ed in t:o to th)ee cla'' 'e''ion'- Mo't 'tudent' ha.e had &)e.iou' e*&o'u)e to 'ingle 'um &)o+lem' and o)dina)y annuitie'/ +ut annuitie' due and defe))ed annuitie' :ill +e ne: mate)ial fo) mo't 'tudent'- The fi)'t cla'' 'e''ion can +e u'ed fo) di'cu''ing Illu't)ation 63TEACHING TIP
Illu't)ation 63 can +e di't)i+uted to 'tudent' a' a 'elfcontained 6&age handoutIt u'e' ,; 'am&le &)o+lem' to demon't)ate a 2'te& 'olution method that can +e u'ed to 'ol.e any of the &)o+lem' di'cu''ed in the cha&te)Some 'tudent' :ith a +ac9g)ound in math o) finance cou)'e' may &)efe) to u'e e*&onential fo)mula' )athe) than inte)e't ta+le' to find inte)e't facto)'!the) 'tudent' :ith 'o&hi'ticated calculato)' may &)efe) to let the calculato) do the :o)9- Remind 'tudent' that :hethe) they u'e inte)e't ta+le'/ e*&onential fo)mula'/ o) inte)nal calculato) )outine'/ they cannot 'ol.e &)o+lem' co))ectly unle'' they can co))ectly identify the ty&e of &)o+lem/ the num+e) of &e)iod'/ and the inte)e't )ate in.ol.ed- Student' often ha.e no difficulty :ith &)o+lem' that a)e :o)ded8 At 6J/ :hat i' the &)e'ent .alue of an annuity due of 0; &ayment' of ,;/;;; eachO +ut they may not 9no: ho: to &)oceed if the 'ame &)o+lem i' :o)ded8 hat amount mu't +e de&o'ited no: in an account &aying ,0J if it i' de'i)ed to ma9e 0; 'emiannual :ithd)a:al' of ,;/;;; each/ +eginning todayO Em&ha'ie to 'tudent' the im&o)tance of &)o&e)ly 'etting u& the &)o+lemThe 'econd and thi)d cla'' 'e''ion' can +e u'ed fo) dete)mining 'olution' to mo)e com&le* &)o+lem'/ including defe))ed annuitie'/ +ond .aluation and othe) accounting a&&lication'- Some of the =ou)nal ent)ie' fo) the accounting a&&lication' can +e di'cu''ed +)ieflyThe follo:ing lectu)e outline i' a&&)o&)iate fo) thi' cha&te)A- #L-!- ,% Int)oduction,- >i'cu'' the im&o)tance of the time .alue of money0- >e'c)i+e accounting a&&lication' of time .alue conce&t'8 +ond'/ &en'ion'/ lea'e'/ longte)m note'1- >e'c)i+e &e)'onal a&&lication' of time .alue conce&t'8 &u)cha'ing a home/ &lanning fo) )eti)ement/ e.aluating alte)nati.e in.e'tment'"- #L-!- ,% Natu)e of Inte)e't-
6,;Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
,- Inte)e't i' &ayment fo) the u'e of money- It i' the e*ce'' ca'h )ecei.ed o) )e&aid o.e) and a+o.e the &)inci&al #amount lent o) +o))o:ed%0- Inte)e't )ate' a)e 'tated on an annual +a'i' unle'' indicated othe):i'e-
Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 6,,
C- #L-!- 0% Sim&le Inte)e'tTEACHING TIP
Illu't)ation 6, can +e u'ed to di'tingui'h +et:een 'im&le inte)e't and com&ound inte)e't,-
Sim&le inte)e't i' com&uted on the amount of the &)inci&al only-
0- Sim&le inte)e't & i n :he)e & &)inci&ali )ate of inte)e't fo) a 'ingle &e)iodn num+e) of &e)iod'-
>- #L-!- 0% Com&ound Inte)e't,- Com&ound inte)e't i' com&uted on the &)inci&al and on any inte)e't ea)ned that ha' not +een &aid o) :ithd)a:n0- >i'cu'' the &o:e) of time and com&ounding- #E-g-/ hat do the num+e)' meanO on te*t &age 065 indicate' that at 3J com&ounded annually/ ,/;;; g)o:' to 01/714 in 63 yea)'- At 3J 'im&le inte)e't/ ,/;;; :ould g)o: to only 2/03; in 63 yea)'-% 2/03; ,/;;; Q #,/;;; -;3 63%1- The te)m &e)iod 'hould +e u'ed in'tead of yea)'a-
Inte)e't may +e com&ounded mo)e than once a yea)8 If inte)e't i' com&ounded Annually Semiannually (ua)te)ly Monthly
+-
Num+e) of com&ounding &e)iod' &e) yea) , 0 2 ,0
Ad=u'tment :hen inte)e't i' com&ounded mo)e than once a yea)#,% Com&ute the com&ounding &e)iod inte)e't )ate8 di.ide the annual inte)e't )ate +y the num+e) of com&ounding &e)iod' &e) yea)#0% Com&ute the total num+e) of com&ounding &e)iod'8 multi&ly the num+e) of yea)' +y the num+e) of com&ounding &e)iod' &e) yea)-
6,0Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 6,1
E- #L-!- 1% 'e of Com&ound Inte)e't Ta+le',- The ta+le' contain inte)e't facto)' that 'im&lify the com&utation of com&ound inte)e't- E*am&le8 If ,/;;; i' de&o'ited today at 4J com&ound inte)e't/ the +alance in 1 yea)' can +e dete)mined8 a- "y )e&etiti.e calculation i)'t yea)8 ,/;;; Q #,/;;; -;4% ,/;4;Second yea)8 ,/;4; Q #,/;4; -;4% ,/,77Thi)d yea)8 ,/,77 Q #,/,77 -;4% ,/043 #)ounded%+- "y u'e of e*&onential fo)mula' ,/;;; #,-;4%1 ,/043 #)ounded%c-
"y u'e of inte)nal calculato) )outine' o) com&ute) &)og)am'-
d- "y o+taining the ,-043;1 inte)e't facto) f)om Ta+le 6, fo) 1 &e)iod' at 4J and &e)fo)ming the a&&)o&)iate com&utation ,/;;; ,-043;1 ,/043-;10-
>e'c)i+e the fi.e inte)e't ta+le' &)o.ided in the te*t8 a-
Ta+le 6,8 utu)e Value of ,-
+-
Ta+le 608 P)e'ent Value of ,-
c-
Ta+le 618 utu)e Value of an !)dina)y Annuity of ,-
d-
Ta+le 628 P)e'ent Value of an !)dina)y Annuity of ,-
e-
Ta+le 638 P)e'ent Value of an Annuity >ue of ,-
- #L-!- 2% Te)minology 'ed in Com&ound Inte)e't P)o+lem',- >e'c)i+e the fou) fundamental .a)ia+le' in com&ound inte)e't &)o+lem'8 TEACHING TIP
Illu't)ation 60 de&ict' a time diag)am that identifie' the fou) .a)ia+le' that a)e fundamental to all com&ound inte)e't &)o+lem'- Illu't)ation 61 can +e u'ed to 'ho: 'tudent' ho: the fou) fundamental .a)ia+le' )elate to the time .alue of money conce&t'a- Rate of inte)e't+-
Num+e) of time &e)iod'-
6,2Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
c-
utu)e .alue-
d- P)e'ent .alue0- >e'c)i+e the diffe)ence +et:een 'ingle 'um and annuity &)o+lem'a-
Single 'um &)o+lem' in.ol.e a 'ingle amount of money that eithe) e*i't' no: o) :ill in the futu)e-
+-
Annuity &)o+lem' in.ol.e a 'e)ie' of eual &e)iodic &ayment' o) )ecei&t' called )ent'#,% In an o)dina)y annuity the )ent' occu) at the end of each &e)iod- The fi)'t )ent :ill occu) one &e)iod f)om no:#0% In an annuity due the )ent' occu) at the +eginning of each &e)iod- The fi)'t )ent :ill occu) no:-
G- Ste&' in Sol.ing Com&ound Inte)e't P)o+lem'TEACHING TIP
'e Illu't)ation 62 to di'cu'' the 3'te& 'olution method that can +e u'ed to 'ol.e any com&ound inte)e't &)o+lemEm&ha'ie the im&o)tance of &e)fo)ming Ste&' , and 0 co))ectlyhethe) 'tudent' u'e inte)e't ta+le'/ e*&onential fo)mula'/ o) calculato) )outine'/ they cannot 'ol.e &)o+lem' co))ectly unle'' they can co))ectly identify the ty&e of &)o+lem/ the num+e) of &e)iod'/ and the inte)e't )ate in.ol.edH- #L-!- 3% S&ecific P)o+lem'Single Sum P)o+lem'TEACHING TIP
P)o+lem' ,/ 0/ and 1 in Illu't)ation 63 demon't)ate 'ingle 'um &)o+lem 'ituation',- o)mula fo) futu)e .alue8 utu)e .alue &)e'ent .alue #o) amount% futu)e .alue facto) fo) n &e)iod' at i J V PV #V n / i %
0- o)mula fo) &)e'ent .alue8
Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 6,3
P)e'ent .alue futu)e .alue * &)e'ent .alue facto) fo) n &e)iod' at iJ PV V #PV n / i %
1-
Point out that the &)e'ent .alue i' al:ay' a 'malle) uantity than the futu)e .alue2- The &)oce'' of finding the futu)e .alue i' called accumulation com&ounding- The &)oce'' of finding the &)e'ent .alue i' called di'counting3-
The facto)' in Ta+le 60 a)e the )eci&)ocal of co))e'&onding facto)' in Ta+le 6,- The)efo)e/ all 'ingle 'um &)o+lem' can +e 'ol.ed +y u'ing eithe) Ta+le 6, o) 60- o) e*am&le/ if the futu)e .alue i' 9no:n and the &)e'ent .alue i' to +e 'ol.ed fo)/ the &)e'ent .alue can +e found8 a- +y multi&lying the 9no:n futu)e .alue +y the a&&)o&)iate facto) f)om Ta+le 60/ o) +-
+y di.iding the 9no:n futu)e .alue +y the a&&)o&)iate facto) f)om Ta+le 60-
I- #L-!- 6 and 5% S&ecific P)o+lem'!)dina)y Annuitie'TEACHING TIP
P)o+lem' 2/ 3/ and 7 in Illu't)ation 63 demon't)ate o)dina)y annuity &)o+lem 'ituation',- o)mula fo) futu)e .alue of an o)dina)y annuity8 utu)e .alue of o)dina)y annuity &e)iodic )ent futu)e .alue of o)dina)y annuity facto) fo) n &e)iod' at i J V!A R #V F !An / i %
0- o)mula fo) &)e'ent .alue of an o)dina)y annuity8 P)e'ent .alue of o)dina)y annuity &e)iodic )ent &)e'ent .alue of o)dina)y annuity facto) fo) n &e)iod' at i J PV!A R #PV F !An / i %
6,6Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
1- Point out that the &)e'ent .alue of an o)dina)y annuity i' al:ay' 'malle) than the futu)e .alue of a 'imila) annuity2-
The facto)' in Ta+le' 61 and 62 a)e not )eci&)ocal' of each othe)-
3- In annuity &)o+lem'/ the )ent'/ inte)e't &ayment'/ and num+e) of &e)iod' mu't all +e 'tated on the 'ame +a'i'- o) e*am&le/ if inte)e't i' com&ounded 'emiannually/ then n the num+e) of 'emiannual )ent' &aid o) )ecei.ed/ i the annual inte)e't )ate di.ided +y 0/ and R the amount of )ent &aid o) )ecei.ed e.e)y 6 month'-
Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 6,5
6- Some confu'ion may a)i'e in annuity &)o+lem' +ecau'e of t:o diffe)ent meaning' of the :o)d &e)iod- a-
o) the &u)&o'e of loo9ing u& inte)e't facto)'/ n eual' the num+e) of &e)iod' and i' al:ay' eual to the num+e) of )ent'-
+- In the &h)a'e :hen com&uting the futu)e .alue of an o)dina)y annuity the num+e) of com&ounding &e)iod' i' one le'' than the num+e) of )ent'/ the te)m &e)iod' )efe)' to com&ounding &e)iod' o) inte)e't+ea)ing &e)iod'- Thi' )efe)' to the num+e) of time' inte)e't i' ea)ned on the &)inci&al and any accumulated inte)e't- Thi' u'age of the te)m &e)iod i' u'eful fo) di'tingui'hing +et:een o)dina)y annuitie' and annuitie' due- Thi' u'age i' intended to e*&lain :hy the ad=u'tment of facto)' f)om Ta+le 61 i' done the :ay it i' :hen the &)o+lem in.ol.e' the futu)e .alue of an annuity due@- #L-!- 6 and 5% S&ecific P)o+lem'Annuitie' >ueTEACHING TIP
P)o+lem' 6 and 5 in Illu't)ation 63 demon't)ate annuity due &)o+lem 'ituation',- o)mula fo) futu)e .alue of annuity due8 utu)e .alue of annuity due &e)iodic )ent * futu)e .alue of o)dina)y annuity facto) fo) n &e)iod' at i J #, Q i % VA> R #V F !An / i % #, Q i %
a-
An inte)e't ta+le i' not &)o.ided fo) the futu)e .alue of an annuity due-
+- E*am&le8 At 4J/ :hat i' the futu)e .alue of an annuity due of 5 &ayment' of 1/;;; eachO 1/;;; 4-0;;22 ,-;4 1;/;73-22 0- o)mula fo) &)e'ent .alue of annuity due8 P)e'ent .alue of annuity due &e)iodic )ent * &)e'ent .alue of annuity due facto) fo) n &e)iod' at i J PVA> R #PV F A> n / i %
6,7Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
1-
Point out that8 a- The &)e'ent .alue of an annuity due i' al:ay' 'malle) than the futu)e .alue of a 'imila) annuity due+-
The futu)e .alue #&)e'ent .alue% of an annuity due i' al:ay' la)ge) than the futu)e .alue #&)e'ent .alue% of a 'imila) o)dina)y annuity :ith the 'ame inte)e't )ate and num+e) of )ent'-
- #L-!- 7% S&ecific P)o+lem'>efe))ed Annuitie'TEACHING TIP
P)o+lem' 4 and ,; in Illu't)ation 63 demon't)ate defe))ed annuity &)o+lem 'ituation',- A defe))ed annuity doe' not +egin to &)oduce )ent' until t:o o) mo)e &e)iod' ha.e e*&i)ed0- A defe))ed annuity &)o+lem can occu) in eithe) an o)dina)y annuity 'ituation o) an annuity due 'ituationa-
In o)de) to 9ee& the &)e'entation 't)aightfo):a)d/ only the o)dina)y annuity 'ituation ha' +een illu't)ated in the te*t and in Illu't)ation 63-
+-
The diffe)ence' +et:een the t:o 'ituation' a)e a' follo:'8 !)dina)y Annuity of n Rent' >efe))ed fo) y Pe)iod'
Annuity >ue of n Rent' >efe))ed
#y Q ,% &e)iod' f)om no:
y &e)iod' f)om
La't )ent occu)'
#y Q n % &e)iod' f)om no:
#y Q n F ,% &e)iod' f)om no:
utu)e .alue i' mea'u)ed a' of
immediately afte) the la't )ent
one &e)iod afte) the la't )ent
fo)
y Pe)iod'
i)'t )ent occu)'
no:
c- If a defe))ed annuity in.ol.e' 'ol.ing fo) a &)e'ent .alue/ the di'tinction +et:een an o)dina)y annuity and an annuity due ha' no &)actical 'ignificance- #i-e-/ 'ee P)o+lem ,; in Illu't)ation 63- Thi' can +e 'et u& eithe) a' the &)e'ent .alue of an o)dina)y annuity of 2 )ent' defe))ed 1 &e)iod'/ a' :a' done in Illu't)ation 63/ o) it can +e 'et u& a' the &)e'ent .alue of an annuity due of 2 )ent' defe))ed
Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual 6,4
2 &e)iod'- If the latte) i' done/ diffe)ent com+ination' of facto)' :ill +e u'ed/ +ut the 'ame an':e) :ill +e o+tained-%
60; Manual
Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D'
d-
Ho:e.e)/ if a defe))ed annuity in.ol.e' 'ol.ing fo) a futu)e .alue/ the di'tinction +et:een an o)dina)y annuity and an annuity due i' im&o)tant- The follo:ing fo)mula i' )eui)ed8 VA> F d R #V F !An / i % #, Q i % :he)e VA> F d futu)e .alue of an annuity due of n )ent' defe))ed fo) y &e)iod' R &e)iodic )ent'
#V F !An / i % facto) f)om Ta+le 61 fo) n &e)iod' at i J #, Q i % , &lu' the inte)e't )ate To illu't)ate/ 'u&&o'e P)o+lem 4 in Illu't)ation 63 had +een :o)ded a' follo:'8 A' of the +eginning of hi' fi)'t yea) in college/ a 'tudent &lan' to de&o'it ,/;;; in an 7J account at the end of hi' thi)d/ fou)th/ and fifth yea)' in 'chool- hat :ill +e the +alance in the account one yea) afte) the la't de&o'itO The time diag)am fo) thi' )e.i'ed &)o+lem i'8
0
1
2
1,000
1,000
1,000
3
4
5
6
The )e.i'ed &)o+lem in.ol.e' 'ol.ing fo) the futu)e .alue of an annuity due of 1 )ent' defe))ed fo) 1 &e)iod'- The 'olution i' VA> F d R #V F !A1/-7J% #,-;7% ,/;;; 1-0262;
,-;7 1/3;6-,,To 'um u&8 In 'ol.ing fo) the futu)e .alue of a defe))ed annuity #,% If the futu)e .alue i' to +e dete)mined immediately afte) the la't )ent/ the &)o+lem may +e thought of a' an o)dina)y annuityThe com&utation de'c)i+ed in the te*t and in Illu't)ation 63 i' adeuate#0% If the futu)e .alue i' to +e dete)mined one &e)iod afte) the la't )ent/ the &)o+lem 'hould +e thought of a' an annuity due- An Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
0,
6
ad=u'tment mu't +e made to accumulate inte)e't fo) one mo)e &e)iod-
600 Manual
Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D'
L- #L-!- 7% S&ecific P)o+lem'"ond Valuation P)o+lem',- >i'cu'' the di'tinction +et:een the 'tated )ate of inte)e't and the ma)9et o) effecti.e yield )ate of inte)e't8 a-
The 'tated inte)e't )ate i' u'ed to dete)mine the &e)iodic amount of ca'h inte)e't &aid-
+-
The ma)9et o) effecti.e inte)e't )ate i' u'ed to .alue the +ond'Thi' i' the )ate :hich i' loo9ed u& in the &)e'ent .alue ta+le'-
0- The e*am&le in the te*t demon't)ate' .aluation of +ond' :hich &ay inte)e't annuallyTEACHING TIP
Illu't)ation 66 &)o.ide' an e*am&le of a +ond .aluation &)o+lem in :hich +ond inte)e't i' &aid 'emiannuallyM- #L-!- 4% E*&ected ca'h flo: a&&)oach,-
Int)oduced +y IAS No- 16-
0-
'e' a )ange of ca'h flo:' and thei) )elated &)o+a+ilitie' to &)o.ide a mo)e )ele.ant mea'u)ement of &)e'ent .alue-
1- Choo'ing an a&&)o&)iate inte)e't )ate8 a- i' not al:ay' o+.iou'+- th)ee com&onent' of inte)e't8 #,% &u)e )ate of inte)e't #0JF2J%#0% e*&ected inflation )ate of inte)e't #;JFOJ%#1% c)edit )i'9 )ate of inte)e't #;JF3J%TEACHING TIP
'e Illu't)ation 65 to &)o.ide a +a'i' fo) di'cu''ing ho: to a&&ly the e*&ected ca'h flo: a&&)oach-
Co&y)ight ? 0;,, @ohn iley B Son'/ Inc- ie'o/ Inte)mediate8 IRS Edition/ In't)ucto)D' Manual
01
6
ILLSTRATI!N 6, SIMPLE INTEREST VS- C!MP!N> INTEREST
602 Manual
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ILLSTRATI!N 60 N>AMENTAL VARIA"LES IN C!MP!N> INTEREST PR!"LEMS
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03
6
ILLSTRATI!N 61 TIME >IAGRAMS
606 Manual
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ILLSTRATI!N 62 STEPS IN S!LVING C!MP!N> INTEREST PR!"LEMS
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05
6
ILLSTRATI!N 63 EAMPLES ! C!MP!N> INTEREST PR!"LEMS
607 Manual
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04
6
ILLSTRATI!N 63 #continued%
61; Manual
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1,
6
ILLSTRATI!N 63 #continued%
610 Manual
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6
ILLSTRATI!N 63 #continued%
612 Manual
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6
ILLSTRATI!N 63 #continued%
616 Manual
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ILLSTRATI!N 63 #continued%
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6
617 Manual
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ILLSTRATI!N 66 "!N> VALATI!N
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6
ILLSTRATI!N 65 EPECTE> CASH L!S AN> PRESENT VALE
62; Manual
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