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A B C D E F G H I J K L
PROBLEM 2.42
i= 6.00%
a$8,000
$2X
b
X= $2,272.61 <–SOLVER CHANGED CELL
P= $8,000.00 <–SOLVER TARGET CELL
USING EXCEL’S PV AND NPV FUNCTIONS THIS IS
TO SOLVE FOR THE VALUE OF X, SET UP THE PRESENT WORTH OF RENALDO’S
PAYMENTS AS A FUNCTION OF X AND LET X BE ANY MONETARY VALUE FOR NOW.
THEN, USE SOLVER TO SET THE PW OF PAYMENTS EQUAL TO $8,000.
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A B C D E F G H I J K L
CAN ALSO SOLVE USING INTEREST TABLES.
P= $8,000 USING INTEREST TABLES THIS IS
=$X*(P|F 6%,5)+($X+$100)*(P|F 6%,6)+($X+$400)*(P|F 6%,7)+$2X*(P|F 6%,8)
=$X*(0.74726)+($X+$100)*(0.70496)+($X+$400)*(0.66506)+$2X*(0.62741)
=3.37210*X+$336.52
X= $2,272.61 =(8000-336.52)/3.3721
c EOY PAYMENT
5$2,272.61 $X
6$2,372.61 $X+100
7$2,672.61 $X+400
8$4,545.23 $2X
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USING INTEREST TABLES THIS IS
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A B C D E F G H I J
USING INTEREST TABLES THIS IS
PROBLEM 2.43
i= 8.00%
n= 6
EOY 0 1 2 3 4 5 6
NCF $0.00 $500.00 -$200.00 $600.00 $300.00 -$100.00 $200.00
aP= $1,046.28 USING EXCEL’S NPV FUNCTION THIS IS
=NPV(6.5%,-500,200,400,-300,500,-200,100)+0
$1,046.28
USING INTEREST TABLES THIS IS
bF= $1,660.31 USING EXCEL’S FV FUNCTION THIS IS
$1,660.31
USING INTEREST TABLES THIS IS
cP= $1,046.28 CONVERTING THE FW TO PW USING EXCEL’S PV FUNCTION
=$1,660.31*(P|F 8%,6)
=$1,423.45*(P|F 8%,4)
=FV(6.5%,6,,500)+FV(6.5%,5,,-200)+FV(6.5%,4,,-
400)+FV(6.5%,3,,300)+FV(6.5%,2,,-500)+FV(6.5%,1,,200)+100
=$500*(F|P 8%,5)-$200*(F|P 8%,4)+$600*(F|P 8%,3)+$300*(F|P
8%,2)-$100*(F|P 8%,1)+$200
=$500*(P|F 8%,1)-$200*(P|F 8%,2)+$600*(P|F 8%,3)+$300*(P|F
8%,4)-$100*(P|F 8%,5)+$200*(P|F 8%,6)
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A B C D E F G H
PROBLEM 2.44
i= 12.00%
COST $30,000.00
PAYMENT METHOD 1
GET CASH DISCOUNT=
3.00%
PW= $29,100.00 =30000*(1-0.03)
PAYMENT METHOD 2
PAY ACCORDING TO THE FOLLOWING SCHEDULE
EOY 0 1 2 3 4 5
CF $5,000.00 $8,000.00 $6,000.00 $6,000.00 $6,000.00 $6,000.00
PW= $28,414.37 USING EXCEL’S NPV FUNCTION THIS IS
=NPV(12%,8000,6000,6000,6000,6000)+5000
PW= $28,414.40 USING INTEREST TABLES THIS IS
USE PAYMENT METHOD 2 – LOWER PW
=$5,000+$8,000*(P|F 12%,1)+$6,000*(P|F
12%,2)+$6,000*(P|F 12%,3)+$6,000*(P|F
12%,4)+$6,000*(P|F 12%,5)
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A B C D E F G H I J K
PROBLEM 2.45
i= 5.50%
a$5X
$4X
$3X
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$1,900.97
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c EOY
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d SUM
INTEREST =28,514.50-20,000.00
AMOUNT OF KEN’S CHECK
$28,514.50
$8,514.50
$1,900.97
$3,801.93
$5,702.90
$7,603.87
$9,504.83
PAYMENT
PROBLEM 2.46
ai= 8.00%
PERIOD t1 2 3
DEPOSIT $1,200.00 $500.00 $2,000.00
FW(3)= $3,939.68 USING COMPOUND INTEREST FORMULAS
=1200*(1+0.08)^2+500*(1.08)+2000
FW(3)= $3,939.68 USING INTEREST TABLES
=1200*(F|P 8%,2)+500*((F|P 8%,1)+2000
FW(3)= $3,939.68 USING EXCEL’S FV FUNCTION
=FV(8%,2,,-1200)+FV(8%,1,,1)+2000
bi= 8.00%
PERIOD t1 2 3
DEPOSIT $1,200.00 $500.00 $2,000.00
FW(6)= $4,962.86 USING COMPOUND INTEREST FORMULAS
=1200*(1+0.08)^5+500*(1.08)^4+2000*(1+0.08)^3
FW(6)= $4,962.86 USING INTEREST TABLES
=1200*(F|P 8%,5)+500*((F|P 8%,4)+2000*(F|P 8%,3)
FW(6)= $4,962.86 USING EXCEL’S FV FUNCTION
=FV(8%,5,,-1200)+FV(8%,4,,-500)+FV(8%,3,,-2000)
PROBLEM 2.47
AT THE END OF 8 YEARS, THE BALANCE IN THE FUND IS
F8 = $1,000(F|P 8%,8) + $3,000(F|P 8%,6) + $4,000(F|P 8%,4)
= $1,000(1.85093) + $3,000(1.58687) + $4,000(1.36049) 12053.5
= $12,053.50
THE ACCUMULATED INTEREST EQUALS $12,053.50-($1,000+$3,000+$4,000) OR $4,053.50.
$4,053.50 IS DEPOSITED IN THE 10% FUND. IT ACCUMULATES IN 4 YEARS TO A VALUE OF:
F = $4,053.50(F|P 10%,4) = $4,053.50(1.4641) = $5,934.73
IN THE ORIGINAL FUND, THE BALANCE IN 4 MORE YEAS WILL BE:
F = $8,000(F|P 8%,4) = $8,000(1.36049) = $10,883.92
USING EXCEL’S FV AND NPV FUNCTIONS, THE BALANCE IN THE FUND AT THE END OF 8 YEARS IS
$12,053.51 =FV(8%,9,,-NPV(8%,1000,0,3000,,4000))
OR
EOY CASH FLOW
0$0
1 $1,000
2$0
3 $3,000
4$0
5 $4,000
6$0
7$0
8$0
9$0
$6,029.76 =NPV(8%,C18:C26)
$12,053.51 =FV(8%,9,,-C27)
USING EXCEL’S FV FUNCTION, THE BALANCE IN THE ORIGINAL FUND AT THE END OF 12 YEARS IS
$10,883.91 =FV(8%,4,,-8000)
USING EXCEL’S FV FUNCTION, THE BALANCE IN THE 10% FUND AT THE END OF 12 YEARS IS
$5,934.74 =FV(8%,4,,-8000)
PROBLEM 2.48
i= 10.00%
n= 4
P= $1,000.00
TO FIND THE SIZE OF THE LOAN PAYMENT
A= $315.47 USING COMPOUND INTEREST FORMULAS THIS IS
=1000*0.1*(1.1^4)/(1.1^4-1)
A= $315.47 USING INTEREST TABLES THIS IS
=$1,000*(A|P 10%,4)
A= $315.47 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(10%,4,-1000)
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A B C D E F G H I
PROBLEM 2.49
P|A FACTOR
i= 8.00% USING 8% FOR EXAMPLE CALC
n= 8 USING 8 FOR EXAMPLE CALC
(P|A i%,n)=
5.74664 USING COMPOUND INTEREST FORMULAS THIS IS
=((1+0.08)^8-1)/(0.08*(1+0.08)^8)
A|P FACTOR
i= 3.00% USING 3% FOR EXAMPLE CALC
n= 5 USING 5 FOR EXAMPLE CALC
(A|P i%,n)=
0.21835 USING COMPOUND INTEREST FORMULAS THIS IS
=(0.03*(1+0.03)^5)/((1+0.03)^5-1)
F|A FACTOR
i= 10.00% USING 10% FOR EXAMPLE CALC
n= 10 USING 10 FOR EXAMPLE CALC
(F|A i%,n)= 15.93742 USING COMPOUND INTEREST FORMULAS THIS IS
=((1+0.1)^10-1)/0.1
A|F FACTOR
i= 3.00% USING 3% FOR EXAMPLE CALC
n= 5 USING 5 FOR EXAMPLE CALC
(A|F i%,n)= 0.18835 USING COMPOUND INTEREST FORMULAS THIS IS
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PROBLEM 2.50
i= 6.00%
n= 8
A= $7,500.00
P= $46,573.45 USING COMPOUND INTEREST FORMULAS THIS IS
=7500*((1+0.06)^8-1)/(0.06*(1+0.06)^8)
P= $46,573.43 USING INTEREST TABLES THIS IS
=$7,500*(P|A 6%,8)
P= $46,573.45 USING EXCEL’S PV FUNCTION THIS IS
=PV(6%,8,-7500)
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=7500*((1+0.04)^20-1)/0.04
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A B C D E F G H I J K L M N O
PROBLEM 2.51
ai= 4.00%
n= 20
A= $7,500.00
F= $223,335.59 USING COMPOUND INTEREST FORMULAS THIS IS
F= $223,335.60 USING INTEREST TABLES THIS IS
=$7,500*(F|A 4%,20)
F= $223,335.59 USING EXCEL’S FV FUNCTION THIS IS
=FV(0.04,20,-7500)
i= 4.00%
n= 25
A= $7,500.00
F= $312,344.31 USING COMPOUND INTEREST FORMULAS THIS IS
=7500*((1+0.04)^25-1)/0.04
F= $312,344.33 USING INTEREST TABLES THIS IS
=$7,500*(F|A 4%,25)
F= $312,344.31 USING EXCEL’S FV FUNCTION THIS IS
=FV(0.04,25,-7500)
i= 4.00%
n= 30
A= $7,500.00
F= $420,637.03 USING COMPOUND INTEREST FORMULAS THIS IS
=7500*((1+0.04)^30-1)/0.04
F= $420,637.05 USING INTEREST TABLES THIS IS
=$7,500*(F|A 4%,30)
F= $420,637.03 USING EXCEL’S FV FUNCTION THIS IS
=FV(0.04,30,-7500)
bi= 5.00%
n= 20
A= $7,500.00
F= $247,994.66 USING COMPOUND INTEREST FORMULAS THIS IS
=7500*((1+0.05)^20-1)/0.05
F= $247,994.63 USING INTEREST TABLES THIS IS
=$7,500*(F|A 5%,20)
F= $247,994.66 USING EXCEL’S FV FUNCTION THIS IS
=FV(0.05,20,-7500)
i= 5.00%
n= 25
A= $7,500.00
F= $357,953.24 USING COMPOUND INTEREST FORMULAS THIS IS
=7500*((1+0.05)^25-1)/0.05
F= $357,953.25 USING INTEREST TABLES THIS IS
=$7,500*(F|A 5%,25)
F= $357,953.24 USING EXCEL’S FV FUNCTION THIS IS
=FV(0.05,25,-7500)
i= 5.00%
n= 30
A= $7,500.00
F= $498,291.36 USING COMPOUND INTEREST FORMULAS THIS IS
=7500*((1+0.05)^30-1)/0.05
F= $498,291.38 USING INTEREST TABLES THIS IS
=$7,500*(F|A 5%,30)
F= $498,291.36 USING EXCEL’S FV FUNCTION THIS IS
=FV(0.05,30,-7500)
c PERCENTAGE INCREASE FROM 20 TO 25 YEARS AT 4%=
39.85% =(312344.31-223335.59)/223335.59
PERCENTAGE INCREASE FROM 20 TO 30 YEARS AT 4%=
88.34% =(420637.03-223335.59)/223335.59
PERCENTAGE INCREASE FROM 20 TO 25 YEARS AT 5%=
44.34% =(357953.24-247994.66)/247994.66
PERCENTAGE INCREASE FROM 20 TO 30 YEARS AT 5%=
100.93% =(498291.36-247994.66)/247994.66
PERCENTAGE INCREASE FROM 4% TO 5% FOR 20 YEARS=
11.04% =(247994.66-223335.59)/223335.59
PERCENTAGE INCREASE FROM 4% TO 5% FOR 25 YEARS=
14.60% =(357953.24-312344.31)/312344.31
PERCENTAGE INCREASE FROM 4% TO 5% FOR 30 YEARS=
18.46% =(498291.36-420637.03)/420637.03
AT 4%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 39.85% AND 88.34%, RESPECTIVELY
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AT 5%, 25% AND 50% INCREASES IN YEARS YIELDED INCREASED ACCUMULATIONS OF 44.34% AND 100.93%, RESPECTIVELY
A 25% INCREASE IN INTEREST RATE YIELDED INCREASED ACCUMULATIONS OF 11.04%, 14.60%, AND 18.46%, RESPECTIVELY, FOR 20, 25, AND 30 YEARS
PROBLEM 2.52
ai= 6.00%
n= 5
A= $500.00
F= $2,818.55 USING COMPOUND INTEREST FORMULAS THIS IS
=500*((1+0.06)^5-1)/0.06
F= $2,818.55 USING INTEREST TABLES THIS IS
=$500*(F|A 6%,5)
F= $2,818.55 USING EXCEL’S FV FUNCTION THIS IS
=FV(6%,5,-500)
bi= 6.00%
n= 10
A= $500.00
F= $3,771.85 USING COMPOUND INTEREST FORMULAS THIS IS
=500*(((1+0.06)^5-1)/0.06)*(1+0.06)^5
F= $3,771.86 USING INTEREST TABLES THIS IS
=$500*(F|A 6%,5)*(F|P 6%,5)
F= $3,771.85 USING EXCEL’S FV FUNCTION THIS IS
=FV(C14,5,,FV(C14,5,500))
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A B C D E F
PROBLEM 2.53
ai= 5.00%
n= 10
A= $5,000.00
WITH THE FIRST WITHDRAWAL AT THE END OF YEAR 1
P= $38,608.67 USING COMPOUND INTEREST FORMULAS THIS IS
=5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)
P= $38,608.65 USING INTEREST TABLES THIS IS
=$5,000*(P|A 5%,10)
P= $38,608.67 USING EXCEL’S PV FUNCTION THIS IS
=PV(5%,10,-5000)
bi= 5.00%
n= 10 WITHDRAWALS
t= 3 WITH FIRST WITHDRAWAL AT EOY 3
A= $5,000.00
WITH THE FIRST PAYMENT AT THE END OF YEAR 3
FIND VALUE OF 10 ANNUAL WITHDRAWALS AT EOY 2, THEN FIND PRESENT WORTH
P= $35,019.21 USING COMPOUND INTEREST FORMULAS THIS IS
=5000*((1+0.05)^10-1)/(0.05*(1+0.05)^10)*(1/(1+0.05)^(3-1))
P= $35,019.20 USING INTEREST TABLES THIS IS
$5,000*(P|F 5%,2)*(P|A 5%,10)
P= $35,019.21 USING EXCEL’S PV FUNCTION THIS IS
=PV(5%,3-1,,-PV(5%,10,-5000))
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A B C D E F G H
PROBLEM 2.54
LET’S CONSIDER INTEREST RATES FROM 0% TO 20%
A= $10,000.00 $5,000.00
n= 510
PV OF PV OF
INTEREST 10K FOR 5 YR 5K FOR 10 YR
0.00% $50,000.00 =PV(0%,5,-10000) $50,000.00 =PV(0%,10,-5000)
1.00% $48,534.31 $47,356.52
2.00% $47,134.60 $44,912.93
3.00% $45,797.07 =PV(3%,5,-10000) $42,651.01 =PV(3%,10,-5000)
4.00% $44,518.22 $40,554.48
5.00% $43,294.77 $38,608.67
6.00% $42,123.64 $36,800.44
7.00% $41,001.97 $35,117.91
8.00% $39,927.10 $33,550.41
9.00% $38,896.51 $32,088.29
10.00% $37,907.87 $30,722.84
11.00% $36,958.97 $29,446.16
12.00% $36,047.76 $28,251.12
13.00% $35,172.31 $27,131.22
14.00% $34,330.81 $26,080.58
15.00% $33,521.55 $25,093.84
16.00% $32,742.94 $24,166.14
17.00% $31,993.46 $23,293.02
18.00% $31,271.71 $22,470.43
19.00% $30,576.35 $21,694.67
20.00% $29,906.12 =PV(20%,5,-10000) $20,962.36 =PV(20%,10,-5000)
PREFER TO RECEIVE YOUR MONEY QUICKER AT $10K FOR EACH OF 5 YEARS
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A B C D E
PROBLEM 2.55
i= 5.00%
A1=$1,200.00 YEARS 1-5
n1=5 DEPOSITS YEARS 1-5
A2=-$700.00 YEARS 4-7
n2=4 WITHDRAWALS YEARS 4-7
t2=4 START TIME OF WITHDRAWALS
P= $3,051.18 USING INTEREST TABLES THIS IS
=$1,200*(P|A 5%,5)-$700*(P|A 5%,4)*(P|F 5%,3)
P= $3,051.18 USING EXCEL’S PV FUNCTION THIS IS
=PV(5%,5,-1200)-PV(5%,3,,-PV(5%,4,-700))
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PROBLEM 2.56
i= 7.00%
n= 5
P= $25,000.00
A= $6,097.27 USING COMPOUND INTEREST FORMULAS THIS IS
=25000*(0.07*(1+0.07)^5)/((1+0.07)^5-1)
A= $6,097.25 USING INTEREST TABLES THIS IS
=$25,000*(A|P 7%,5)
A= $6,097.27
USING EXCEL’S PMT FUNCTION THIS IS
=PMT(0.07,5,-25000)
PROBLEM 2.57
i= 10.00%
n= 5
F= $25,000.00
STEP 1 IS TO MOVE THE $25,000 BACK TWO YEARS TO COINCIDE WITH THE FINAL DEPOSIT
P= $20,661.16
Vt=6=25000/1.1^2
P= $20,661.25
Vt=6=$25,000(P|F 10%,2)
P= $20,661.16
Vt=6=PV(10%,2,,-25000)
STEP 2 IS TO CALCULATE THE SIZE OF 5 DEPOSITS TO HAVE THE DESIRED AMOUNT AT t=6
A= $3,384.25 USING COMPOUND INTEREST FORMULAS THIS IS
=20,661.25*0.10/((1+0.10)^5-1)
A= $3,384.31 USING INTEREST TABLES THIS IS
=$25,000*(P|F 10%,2)*(A|F 10%,5)
A= $3,384.25 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(0.10,5,,PV(10%,2,,25000))
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A B C D E F G H
PROBLEM 2.58
ai= 8.00%
n= 8
A= $1,000.00
FINDING THE PW AT EOY 0
P= $5,746.64 USING COMPOUND INTEREST FORMULAS THIS IS
=1000*((1+0.08)^8-1)/(0.08*(1+0.08)^8)
P= $5,746.64 USING INTEREST TABLES THIS IS
=$1,000*(P|A 8%,8)
P= $5,746.64 USING EXCEL’S PV FUNCTION THIS IS
=PV(8%,8,-1000)
bi= 8.00%
n= 8
A= $1,000.00
FINDING THE FW AT EOY 8
F= $10,636.63 USING COMPOUND INTEREST FORMULAS THIS IS
=1000*((1+0.08)^8-1)/0.08
F= $10,636.63 USING INTEREST TABLES THIS IS
=$1,000*(F|A 8%,8)
F= $10,636.63 USING EXCEL’S FV FUNCTION THIS IS
=FV(0.08,8,-1000)
=1000*(((1+0.08)^8-1)/0.08)*(1+0.08)^3
F= $13,399.07 USING INTEREST TABLES THIS IS
=$1,000*(F|A 8%,8)*F|P(8%,3)
F= $13,399.09 USING EXCEL’S FV FUNCTION THIS IS
=FV(8%,11,,PV(8%,8,1000))