Suppose Bank One oers a cercate of deposit thaSuppose Bank One oers a cercate of deposit that pays $5,000 in four years for exchanget pays $5,000 in four years for exchange for $4,
Trang 11 What is thWhat is the future future value of $2e value of $2,000 inv,000 invested tested today if it eaoday if it earns 10% inrns 10% interesterest for one yet for one year?ar? IInnvveessttmmeennt t = = 22,,000000
R
Raatte e = 1100%% Time
Time period period = = 1 1 yearyear Future value = investment (1 + r) t Future value = 2,200
2
2 What is thWhat is the future future value of $2e value of $2,000 inv,000 invested tested today if it eaoday if it earns 10% inrns 10% interesterest for two yet for two years?ars? IInnvveessttmmeennt t = = 22,,000000
R
Raatte e = 1100%% Time
Time period period = = 2 2 yearyear Future value = investment (1 + r) t Future value = 2,420
3
3 What is the futWhat is the future valuure value of $6,000 invee of $6,000 invested tosted today if it earns 8.5day if it earns 8.5% interes% interest for seven Yeat for seven Years?rs? IInnvveessttmmeennt t = = 66,,000000
R
Raatte e = 88 55%% Time
Time period period = = 7 7 yearyear Future value = investment (1 + r) t Future value = 10,621
Trang 24 What is thWhat is the future future value of $6e value of $6,000 inv,000 invested tested today if it eaoday if it earns 8% forns 8% for 10.5 year 10.5 years?rs?
IInnvveessttmmeennt t = = 66,,000000 R
Raatte e = 88 55%% Time
Time period period = = 7 7 yearyear Future value = investment (1 + r) t Future value = 13,462
5
5 An invesAn investor deptor deposiosits $100 into his crets $100 into his credit unidit union accoon accoununt t thathat t papays interys interest at the rate of est at the rate of 3.25% per year (payable at the end of each year) He leaves the money and all accrued interest in the account for 7 years H
interest in the account for 7 years How much will he have at the end ow much will he have at the end of the 7 years?of the 7 years?
IInnvveessttmmeennt t = = 110000 R
Raatte e = 33 2255%% Time
Time period period = = 7 7 yearyear Future value = investment (1 + r) t Future value = 100 (1.0325)7 Future value = 100 (1.251)
Trang 36 WhaWhat is t is ththe future future value in SEVe value in SEVEN yearEN years if s if you recyou receiveive $300 in two yeae $300 in two years and $50rs and $500 at the0 at the end of ve years? Assume an
end of ve years? Assume an annual compound rate of 8.5%.annual compound rate of 8.5%
Future value at end of 7 year
Time investment rate rate of of interest interest me me periodperiod 0
1
3 4 5
7
Future value = 300 ( 1.085 ) 5 + 500 ( 1.085)2 Future value = 300 ( 1.504 ) + 500 (1.77) Future value =451 +589
Future value = 1,040 7
7 What is thWhat is the value of $20e value of $2000 aer on00 aer one year, if bane year, if bank compok compoundinunding half yearg half yearly and oerly and oered rateed rate
is 10%? (note: compare your answer with the answer of queson no.1, give
is 10%? (note: compare your answer with the answer of queson no.1, give comments)comments) IInnvveessttmmeennt t = = 22,,000000
R
Raatte e == 1100% % ppeer r yyeeaarr Time
Time period period = = 1 1 yearyear C
Coommppoouunnddiinngg== hhaallf f yyeeaarrllyy Future value = investment (1 + r/2) t X 2 Future value = 2,205
Trang 48 What is thWhat is the value of $2e value of $2000 ae000 aer one year if br one year if bank comank compounpounding quding quarterarterly and oly and oered raered rate iste is 10%? (note: compare your answer with the answer of queson no.1 and 7, give
10%? (note: compare your answer with the answer of queson no.1 and 7, give comments)comments) IInnvveessttmmeennt t = = 22,,000000
R
Raatte e == 1100% % ppeer r yyeeaarr Time
Time period period = = 1 1 yearyear C
Coommppoouunnddiinngg== qquuaarrtteerrllyy Future value = investment (1 + r/4) t X 4 Future value = 2,208
9
9 What is thWhat is the value of $20e value of $2000a00aer one yeaer one year if bank comr if bank compounpounding moding monthly anthly and oerend oered rate isd rate is 10
10%? %? (n(notote: e: cocompmparare e yoyour ur ananswswer er wiwith th ththe e ananswswer er of of ququesesoon n nono.1.1,7 ,7 anand d 8 8 gigiveve comments)
IInnvveessttmmeennt t = = 22,,000000 R
Raatte e == 1100% % ppeer r yyeeaarr Time
Time period period = = 1 1 yearyear C
Coommppoouunnddiinngg== mmoonntthhllyy Future value = investment (1 + r/12) t X 12
Future value = 2,209
Trang 510 What is the present valuWhat is the present value of e of $2,00$2,000 to 0 to be receivebe received 2 d 2 years froyears from today when the annuam today when the annuall discount rate is 10%
FFuuttuurre e vvaalluue e = = 22,,000000 R
Raatte e == 1100% % ppeer r yyeeaarr Time
Time period period = = 2 2 yearyear C
Coommppoouunnddiinngg== yyeeaarrllyy Present value = Future value / ( 1 + r ) t Present value = 1,653
11
11 What is the present value of $500 to be What is the present value of $500 to be recereceived 10.5 years from today when the annuived 10.5 years from today when the annualal discount rate is 8%?
FFuuttuurre e vvaalluue e = = 550000 R
Raatte e == 88% % ppeer r yyeeaarr Time
Time period period = = 10.5 10.5 yearyear C
Coommppoouunnddiinngg== yyeeaarrllyy Present value = Future value / ( 1 + r ) t Present value = 223
Trang 612 What is the present value of $700 to be received in two equal installments ($350 eaWhat is the present value of $700 to be received in two equal installments ($350 each), twoch), two years and ve years from today, when the annual discount rate is
years and ve years from today, when the annual discount rate is 10%?10%?
Year present present value value rate future future valuevalue
1
3 4
Present value = future va Present value = future value1 lue1 / ( 1 + r ) t + future value2 / ( 1 + r ) / ( 1 + r ) t + future value2 / ( 1 + r ) tt Pr
Presesenent vt valalue ue == 35350/0/(1(1.1.1)2 )2 + 3+ 35050/(/(1.1.1)1)55 Present
Present value value = = 289 289 +217+217 Present
Present value value = = 506
13.Suppose Capitol Federal Bancorp oers a cercate of deposit that pays $10,000 in ve years for exchange for $8,000 today What interest rate is
years for exchange for $8,000 today What interest rate is Capitol Federal Bancorp oering?Capitol Federal Bancorp oering?
FFuuttuurre e vvaalluue e == 1100,,000000 IInnvveessttmmeennt t == 88,,000000 T
Tiimme e ppeerriiood d == 5
( 1 ( 1 + + r r ) ) t t = = future future value value / / present present valuevalue ( 1
( 1+ r + r ) 5) 5== 1010,0,00000/8/8000000 (1 + r ) 5= 1.25
(1 + r ) 5 X (1 + r ) 5 X 1/5 = (1.25) 1/51/5 = (1.25) 1/5
1 + r ) = 1.04
R = 1.04 -1
R = 04 or 4%
Trang 713 Suppose Bank One oers a cercate of deposit thaSuppose Bank One oers a cercate of deposit that pays $5,000 in four years for exchanget pays $5,000 in four years for exchange for $4,000 today What interest rate is Bank
for $4,000 today What interest rate is Bank One oering?One oering?
FFuuttuurre e vvaalluue e == 55,,000000 IInnvveessttmmeennt t == 44,,000000 T
Tiimme e ppeerriiood d == 4 ( 1
( 1 + + r r ) ) t t = = future future value value / / present present valuevalue ( 1
( 1+ r + r ) 4) 4== 5,5,00000/0/40400000
R
R = = 5.74%
14
14 How many years will taHow many years will take $10,000 to grow to $20,00ke $10,000 to grow to $20,000 if bank oered rate is 10%0 if bank oered rate is 10%??
P
n
Using FVIF
FV/PV
n
nln(1+i) = ln(FV/PV) n
n
n
n
15.How many years will take $25,000 to grow to $120,000 if bank oered rate is 18%?
P
n
Using FVIF
Trang 8FFV V= = P PV V [ [ ((1 1 + + i i )) n
n
n
n
n
16
16 Your grandYour grandfathfather placed $2,00er placed $2,000 in 0 in trustrust fund for you t fund for you In 10 In 10 years the fund will be worthyears the fund will be worth
$5,000 What is the compound annual rate of return on the trust
$5,000 What is the compound annual rate of return on the trust fund?fund?
Soluton:
P
n
Using FVIF
17
17 Your rich aunt puts $35,000 into a bank accouYour rich aunt puts $35,000 into a bank account earning 4.00% You are not to withdraw thent earning 4.00% You are not to withdraw the money unl the balance has doubled About how many years will
money unl the balance has doubled About how many years will you have to wait?you have to wait?
P
Using FVIF
n
n
n
Trang 918 Sales of current year are 75,000 aSales of current year are 75,000 and sales of a compannd sales of a company aer four years is $375,000 Whay aer four years is $375,000 Whatt
is the rate of growth?
P
n
Using FVIF
19
19 ConsidConsider an er an APR of APR of 12% with month12% with monthly compounly compoundingding What is the EAR What is the EAR (eec(eecve annuave annuall rate)?
A
m
EAR = ( 1 + 12/ 12
EAR = ( 1 + 01) 12 –
EAR = (1.01 ) 12 – 1 EAR= 1.126 – 1 EAR = 126 EAR = 12.6%
20
20 ConsidConsider an er an APR of APR of 13.5% with quar13.5% with quarterly compoterly compoundinunding What is g What is the EAR (eecve annuathe EAR (eecve annuall rate)?
APR
m
E
E
E
E
Trang 1021 21 CoConsnsidider er an an EAR EAR of of 1313.7.75% 5% wiwith th ququararteterly rly cocompmpououndndining g WhWhat at is is ththe e APAPR R (a(annnnuauall percentage rate)?
m
A
E
A
A
A
%
22 22 CoConsnsidider er an an EAR EAR of of 1818.2.25% 5% wiwith th momontnthlhly y cocompmpououndndining g WhWhat at is is ththe e APAPR R (a(annnnuauall percentage rate)?
m
A
E
APR/m
1/m -1
A
A
A
23
23 Suppose you save $4,000 per year at the end of each year for 3 years and earn 5% interestSuppose you save $4,000 per year at the end of each year for 3 years and earn 5% interest per year How much will you
per year How much will you have at the end of 3 have at the end of 3 years?years?
Future value = investment X FVAFnr Investment = 4,000
Trang 11Raattee== 55%% FVAFnr= ( 1/r-1/r(1+r )t ) X ( 1 + r FVAFnr= ( 1/r-1/r(1+r )t ) X ( 1 + r ) t) t FVAFnr= 3.1525
FVAFnr= 3.1525
24
24 SupSuppospose e you save $4,0you save $4,000 per 00 per yeayear r at the at the end of end of eaceach h yeayear r for 10 for 10 yeayears and earn 8.5%rs and earn 8.5% interest per year How much will you
interest per year How much will you have at the end of 10 have at the end of 10 years?years?
P
n
Using FVAF
25
25 A person deposA person deposited Rs.500ited Rs.5000 at the 0 at the end of six months in each of the next ve years Bankend of six months in each of the next ve years Bank oered rate is 10% Calculate how much he has at
oered rate is 10% Calculate how much he has at the end of ve years.the end of ve years
5,000 n
m
Using FVAF
FV=
Rs.62,889.4 6
26
26 A person saved Rs.2500 at the end A person saved Rs.2500 at the end of each month in the next tof each month in the next three years Bank oered ratehree years Bank oered rate
is 12.25% Calculate how much he has at the
is 12.25% Calculate how much he has at the end of three years.end of three years
Pmt
=
n
m
Trang 12FFV V= = ? Using FVAF
FV
Trang 1327 Suppose you save $4,000 per yeaSuppose you save $4,000 per year at the end of each year for 30 year at the end of each year for 30 years and earn 5% interestrs and earn 5% interest per year How much will you
per year How much will you have at the end of 30 have at the end of 30 years?years?
P
n
Using FVAF
28
28 SupSuppospose e you save $50you save $500 0 per year at the per year at the end of each year for 20 end of each year for 20 yeayears and earn 8.25%rs and earn 8.25% interest per year How much will you
interest per year How much will you have at the end of 20 have at the end of 20 years?years?
P
n
Using FVAF
29
29 SupSuppospose e you savyou save e $1,$1,000 per year at 000 per year at the end of the end of eaceach h yeayear r for 15 for 15 yeayears and earn 8.25%rs and earn 8.25% interest per year How much will you
interest per year How much will you have at the end of 15 have at the end of 15 years?years?
P
n
Using FVAF
Trang 1430 SupSuppospose e you savyou save e $1,$1,000 per year at 000 per year at the end of the end of eaceach h yeayear r for 15 for 15 yeayears and earn 7.49%rs and earn 7.49% interest per year How much will you
interest per year How much will you have at the end of 15 have at the end of 15 years?years?
P
n
Using FVAF
31
31 SupSuppospose e you save $50you save $500 0 per year at the per year at the end of each year for 15 end of each year for 15 yeayears and earn 8.25%rs and earn 8.25% interest per year What is t
interest per year What is the future he future value of this annuvalue of this annuity?ity?
500 n
P
Using PVAF P
P
P
32
32 SuppSuppose that the ose that the consconstantant t and perpetand perpetual cash ow is ual cash ow is $1,0$1,000 and 00 and the discouthe discount rate is nt rate is 8%.8% What is the value of
What is the value of this perpetuity?this perpetuity?
C
P
Using: PV for a perpetuity = cash flow/discount rate
PV=
1,000 / 0.08
Trang 1533 Suppose that the constanSuppose that the constant and perpetual cash ow is $1,000 and the discount rate is 10%.t and perpetual cash ow is $1,000 and the discount rate is 10% What is the value of
What is the value of this perpetuity?this perpetuity?
C
P
Using: PV for a perpetuity = cash flow/discount rate
PV=
1,000 / 0.1
34
34 SuppSuppose you can save $200 per year at the end of each year for 15 years and earn 7.49ose you can save $200 per year at the end of each year for 15 years and earn 7.49%% interest per year However, you
interest per year However, you cannot start saving for ve years What is cannot start saving for ve years What is the present valuethe present value
of this annuity?
35
35 What are the annuaWhat are the annual payments for a 4-year $4,000 loan if the interesl payments for a 4-year $4,000 loan if the interest rate is t rate is 9% per year?9% per year? Make up a loan amorzaon schedule
36
36 You are plannYou are planning to ing to tatake ke a a cacar, its r, its cascash h prprice is ice is Rs.Rs.800800,00,000 Bank 0 Bank is oeriis oering seven yearng seven year monthly payment plan at 18% How much monthly installment will be oered by
monthly payment plan at 18% How much monthly installment will be oered by bank?bank? 37
37 Suppose you are accepng bSuppose you are accepng bank oer as given in Q No.43 but want to amank oer as given in Q No.43 but want to amorze whole loanorze whole loan
in ve years What monthly installment will be
in ve years What monthly installment will be oered by bank?oered by bank?
38
38 SuppSuppose you are planninose you are planning to g to acceaccept bank oer as given in Q pt bank oer as given in Q No.43 but instNo.43 but instead of monthlyead of monthly payment plan, you are interested in quarterly installment Compute theamount you will pay aer each quarter
39
39 Suppose you are planning tSuppose you are planning to take this car through bano take this car through bank loan but you already have saving ok loan but you already have saving of f Rs.150,000 which you paid to bank as down payment and rest you are agree on monthly installment at 18% Compute monthly
installment at 18% Compute monthly payment.payment
40
40 Consider the following Consider the following future value profuture value problem The respecve casblem The respecve cash ows forh ows fort = 0, 1, 2, and 3 are $3,000, $2,000, $8,000, and $5,000 and the discount rate is ten percent What is the future value at t = 4?