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CHAP 5

10. To find the PV of a lump sum, we use:

PV = FV / (1 + r)t 

PV = $650,000,000 / (10!"#0 = $155,%&',"001'

13. To answe this )uestion, we *an use eithe the FV o the PV fomula oth will i-e thesame answe sin*e the. ae the in-ese of ea*h othe e will use the FV fomula, that is:

FV = PV(1 + r #t 

ol-in fo r , we et:

r  = (FV / PV#1 / t   1

r  = ($1,60,000 / $150#1/11

  1 = 0%"0 o %"02

To find the FV of the fist pi3e, we use:

FV = PV(1 + r #t 

FV = $1,60,000(10%"0#'' = $1%,056,"0&&"

 4P 63. To sol-e this po7lem, we must find the FV of ea*h *ash flow and add them To find the

FV of a lump sum, we use:

FV = PV(1 + r)t 

FV8%2 = $&"0(10%#' + $1,0&0(10%# + $1,'"0(10%# + $1,"05 = $5,'0!!1

FV8112 = $&"0(111#' + $1,0&0(111# + $1,'"0(111# + $1,"05 = $5,50&6

FV8"2 = $&"0(1"#' + $1,0&0(1"# + $1,'"0(1"# + $1,"05 = $6,5'"%1

 9oti*e we ae findin the -alue at ea ", the *ash flow at ea " is simpl. added to theFV of the othe *ash flows ;n othe wods, we do not need to *ompound this *ash flow

32. e need to find the annuit. pa.ment in etiement <u etiement sa-ins ends and theetiement withdawals 7ein, so the PV of the etiement withdawals will 7e the FV of 

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the etiement sa-ins o, we find the FV of the sto* a**ount and the FV of the 7onda**ount and add the two FVs

to* a**ount: FV = $!00>?>1 + (11/1# @'60  1A / (11/1#@ = $1,&6',16'%

ond a**ount: FV = $'00>?>1 + (06/1# @'60  1A / (06/1#@ = $'01,'5"51

o, the total amount sa-ed at etiement is:

$1,&6',16'% + '01,'5"51 = $,6",51%''

ol-in fo the withdawal amount in etiement usin the PV e)uation i-es us:

PV = $,6",51%'' = $C >1 ?1 / >1 + (0&/1#@'00A / (0&/1#@C  = $,6",51%'' / 11&1616 = $1&,00'!6' withdawal pe month

66. ee we ae sol-in a twoBstep time -alue of mone. po7lem Ca*h )uestion ass fo adiffeent possi7le *ash flow to fund the same etiement plan Ca*h sa-ins possi7ilit.has the same FV, that is, the PV of the etiement spendin when .ou fiend is ead. toetie The amount needed when .ou fiend is ead. to etie is:

 PV = $105,000?>1 (1/10!#0@ / 0!A = $1,11,'!150

This amount is the same fo all thee pats of this )uestion

a. ;f .ou fiend maes e)ual annual deposits into the a**ount, this is an annuit. withthe FV e)ual to the amount needed in etiement The e)uied sa-ins ea*h .eawill 7e:

FV = $1,11,'!150 = C >(10!'0  1# / 0!@C  = $11,!!601

  b. ee we need to find a lump sum sa-ins amount Dsin the FV fo a lump sume)uation, we et:

FV = $1,11,'!150 = PV(10!#'0 PV = $1"6,1&0"

c. ;n this po7lem, we ha-e a lump sum sa-ins in addition to an annual deposit in*e wealead. now the -alue needed at etiement, we *an su7ta*t the -alue of the lump

sum sa-ins at etiement to find out how mu*h .ou fiend is shot Eoin so i-esus:

FV of tust fund deposit = $150,000(10!#10 = $&5,0!!0

o, the amount .ou fiend still needs at etiement is:

FV = $1,11,'!150 &5,0!!0 = $%1!,&%%0

Dsin the FV e)uation, and sol-in fo the pa.ment, we et:

$%1!,&%%0 = C >(10! '0  1# / 0!@

C  = $%,655

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This is the total annual *onti7ution, 7ut .ou fiends emplo.e will *onti7ute$1,500 pe .ea, so .ou fiend must *onti7ute:

FiendGs *onti7ution = $%,655 1,500 = $!,155