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A B C D E F G H I
PROBLEM 2.78
aF= B*(F|P i%,1)*(F|A i%,n)
bF= B*(1+i)*((1+i)^n-1)/i
cB= $1,000.00
n= 5
i= 10.00%
USING (a) F= $6,715.61 USING INTEREST TABLES THIS IS
=$1,000*(F|P 10%,1)*(F|P 10%,5)
USING (b) F= $6,715.61 USING COMPOUND INTEREST FORMULAS THIS IS
=1000*(1+0.1)*((1+0.1)^5-1)/0.1
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A B C D E F G
PROBLEM 2.79
ai= 5.00%
n= 35
INITIAL CF= $0.00
A1=$7,500.00
G= $1,000.00
n= 35
INITIAL CF= $0.00
A1=$7,500.00
G= $1,000.00
0$0.00 0$0.00
1$7,500.00 1$7,500.00
2$8,500.00 2$8,500.00
3$9,500.00 3$9,500.00
4$10,500.00 4$10,500.00
8$14,500.00 8$14,500.00
9$15,500.00 9$15,500.00
10 $16,500.00 10 $16,500.00
11 $17,500.00 11 $17,500.00
12 $18,500.00 12 $18,500.00
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A B C D E F G
17 $23,500.00 17 $23,500.00
18 $24,500.00 18 $24,500.00
19 $25,500.00 19 $25,500.00
20 $26,500.00 20 $26,500.00
21 $27,500.00 21 $27,500.00
22 $28,500.00 22 $28,500.00
23 $29,500.00 23 $29,500.00
24 $30,500.00 24 $30,500.00
25 $31,500.00 25 $31,500.00
26 $32,500.00 26 $32,500.00
27 $33,500.00 27 $33,500.00
28 $34,500.00 28 $34,500.00
29 $35,500.00 29 $35,500.00
30 $36,500.00 30 $36,500.00
31 $37,500.00 31 $37,500.00
32 $38,500.00 32 $38,500.00
33 $39,500.00 33 $39,500.00
34 $40,500.00 34 $40,500.00
35 $41,500.00 35 $41,500.00
FW= $1,783,808.45 FW= $2,109,673.85
=FV(5%,35,,-NPV(5%,CF YR 1:CF YR 35)+0) =FV(6%,35,,-NPV(6%,CF YR 1:CF YR 35)+0)
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A B C D E F
PROBLEM 2.81
i= 18.00%
n= 5
P= $10,000
G= $700
A|G= 1.67284 USING COMPOUND INTEREST FORMULAS THIS IS
=(1/0.18)-(5/0.18)*(0.18/((1+0.18)^5-1))
OR USING INTEREST TABLES
USING INTEREST TABLES THIS IS
$2,026.81 =$10,000(A|P 18%,5)-$700(A|G 18%,5)
=C6*0.31978-C7*C8
USING EXCEL’S PMT AND NPV FUNCTIONS THIS IS
$2,026.79 =-PMT(C4,5,C6-NPV(C4,0,C7,2*C7,3*C7,4*C7))
PROBLEM 2.82
i= 18.00%
n= 5
A|G= 1.67284 USING COMPOUND INTEREST FORMULAS THIS IS
=(1/0.18)-(5/0.18)*(0.18/((1+0.18)^5-1))
OR USING INTEREST TABLES
P= $10,000.00
G= -$700.00
USING INTEREST TABLES THIS IS
$4,368.79 =$10,000(A|P 18%,5)+$700(A|G 18%,5)
=C9*0.31978-C10*C6
USING EXCEL’S PMT AND NPV FUNCTIONS THIS IS
$4,368.76 =-PMT(C4,5,C9-NPV(C4,0,C10,2*C10,3*C10,4*C10))
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A B C D E F G H I
PROBLEM 2.83
i= 8.00%
n= 6
A1=$12,000.00
G= -$2,000.00
P= $34,428.02 USING INTEREST TABLES THIS IS
=$12,000*(P|A 8%,6)-$2,000*(P|G 8%,6)
P= $34,428.01 USING EXCEL’S NPV FUNCTION
=NPV(8%,12000,10000,8000,6000,4000,2000)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF
0$0.00
1$12,000.00
2$10,000.00
3$8,000.00
4$6,000.00
5$4,000.00
6$2,000.00
P= $34,428.01 =NPV(8%,12000,10000,8000,6000,4000,2000)+0
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A B C D E F G H I
PROBLEM 2.84
i= 6.00%
n= 7
A1=$5,000.00
G= $1,000.00
FV= $65,199.79 USING INTEREST TABLES THIS IS
=($5,000*(P|A 6%,7)+$1,000*(P|G 6%,7))*F|P 6%,7
FV= $65,199.82 USING EXCEL’S FV AND NPV FUNCTIONS
=FV(6%,7,,-NPV(6%,5000,6000,7000,8000,9000,10000,11000))
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF
0 $0.00
1 $5,000.00
2 $6,000.00
3 $7,000.00
4 $8,000.00
5 $9,000.00
6 $10,000.00
7 $11,000.00
FV= $65,199.82 =FV(6%,7,,-(NPV(6%,5000,6000,7000,8000,9000,10000,11000)+0))
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A B C D E F G H
PROBLEM 2.85
i= 5.00%
n= 5
A1=$800.00
G= $100.00
P= $4,287.28 USING INTEREST TABLES THIS IS
=$800*(P|A 5%,5)+$100*(P|G 5%,5)
P= $4,287.27 USING EXCEL’S NPV FUNCTION
=NPV(5%,800,900,1000,1100,1200)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF
0$0.00
1$800.00
2$900.00
3$1,000.00
4$1,100.00
5$1,200.00
P= $4,287.27 =NPV(5%,800,900,1000,1100,1200)+0
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A B C D E F G H
PROBLEM 2.86
ai= 6.00%
n= 8
INITIAL CF= -$75,000.00
A1=$3,000.00
G= $3,000.00
P= $3,154.11 USING INTEREST TABLES THIS IS
n= 8
INITIAL CF= -$75,000.00
A1=$3,000.00
G= $3,000.00
P= -$719.28 USING INTEREST TABLES THIS IS
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A B C D E F G H I
PROBLEM 2.87
i= 12.00%
n= 6
A1=-$2,000.00
G= $1,000.00
P= $707.35 USING INTEREST TABLES THIS IS
-$2,000*(P|A 12%,6)+$1,000*(P|G 12%,6)
P= $707.36 USING EXCEL’S NPV FUNCTION THIS IS
=NPV(12%,-2000,-1000,0,1000,2000,3000)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF
0$0.00
1 -$2,000.00
2 -$1,000.00
3$0.00
4$1,000.00
5$2,000.00
6$3,000.00
P= $707.36
=NPV(12%,-2000,-1000,0,1000,2000,3000)+0
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A B C D E F G H
PROBLEM 2.88
i= 5.00%
n= 5
INITIAL CF= -$90,000.00
A1=$30,000.00
G= -$3,000.00
PW= $15,173.64 USING INTEREST TABLES THIS IS
=-$90,000+$30,000*(P|A 5%,5)-$3,000*(P|G 5%,5)
PW= $15,173.55 USING EXCEL’S NPV FUNCTION THIS IS
=NPV(5%,30000,30000-3000,30000-2*3000,30000-
3*3000,30000-4*3000)-90000
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A B C D E
PROBLEM 2.89
i= 10.00%
n= 10
A1=$7,000.00
G= -$300.00
aP= $36,144.59 USING INTEREST TABLES THIS IS
=$7,000*(P|A 10%,10)-$300*(P|G 10%,10)
F= $93,749.66 USING INTEREST TABLES THIS IS
=$36,144.59*(F|P 10%,10)
F= $93,749.75 USING EXCEL’S FV FUNCTION THIS IS
=FV(10%,10,,-36144.59)
bA= $5,882.36 USING INTEREST TABLES THIS IS
=$7,000-$300*(A|G 10%,10)
A= $5,882.80 USING INTEREST TABLES THIS IS
=$93,749.66*(A|F 10%,10)
A= $5,882.37 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(10%,10,,-93749.75)
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A B C D E F G H
PROBLEM 2.90
i= 6.00%
n= 8
INITIAL CF= -$45,000.00
A1=$12,000.00
G= -$1,000.00
PW= $9,675.90 USING INTEREST TABLES THIS IS
=-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8)
AMT6= $13,725.46 USING INTEREST TABLES THIS IS
=$9,675.90*(F|P 6%,6)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF
0 -$45,000.00
1$12,000.00
2$11,000.00
3$10,000.00
4$9,000.00
5$8,000.00
6$7,000.00
7$6,000.00
8$5,000.00
PW= $9,675.95 USING EXCEL’S NPV FUNCTION THIS IS
AMT6= $13,725.51 USING EXCEL’S FV AND NPV FUNCTIONS THIS IS
=NPV(6%,12000,11000,10000,9000,8000,7000,6000,
5000)-45000
=FV(6%,6,,-
(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5
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A B C D E F G H
PROBLEM 2.91
i= 6.00%
n1=8 YEARS IN ORIGINAL GRADIENT SERIES
INITIAL CF= -$45,000.00
A1=$12,000.00
G= -$1,000.00
t= 3 YEAR BEFORE ANNUAL SERIES FROM 4 TO 7
n2=4 YEARS IN UNIFORM ANNUAL SERIES
PW= $9,675.90 USING INTEREST TABLES THIS IS
=-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8)
AMT3= $11,524.19 USING INTEREST TABLES THIS IS
=$9,675.90*(F|P 6%,3)
A(4-7)= $3,325.77 USING INTEREST TABLES THIS IS
=$11,524.19*(A|P 6%,4)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF
0 -$45,000.00
1 $12,000.00
2 $11,000.00
3 $10,000.00
4 $9,000.00
5 $8,000.00
6 $7,000.00
7 $6,000.00
8 $5,000.00
PW= $9,675.95 USING EXCEL’S NPV FUNCTION THIS IS
AMT3= $11,524.21 USING EXCEL’S FV AND NPV FUNCTIONS THIS IS
A(4-7)= $3,325.79 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(6%,4,-11524.21)
=NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000
=FV(6%,3,,-(NPV(6%,12000,11000,10000,9000,8000,7000,6000,5000)-45000))
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NOW, SET THE GRADIENT AMOUNT “G” TO ANY VALUE AND GO
A B C D E F G H
PROBLEM 2.92
i= 6.00%
n= 8
INITIAL CF= -$45,000.00
A1=$12,000.00
G= -$1,000.00
PW= $9,675.90 USING INTEREST TABLES THIS IS
=-$45,000+$12,000*(P|A 6%,8)-$1,000*(P|G 6%,8)
G= $314.13
THEREFORE
A8=$10,000.00
GIVEN IN PROBLEM
A1=$7,801.07 =10000-7*314.13
3$10,000.00
4$9,000.00
5$8,000.00
6$7,000.00
7$6,000.00
8$5,000.00
NOW, SET UP A NEW GRADIENT SERIES THAT HAS THE SAME PW AS THE
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A B C D E F G H
A8=$10,000.00
GIVEN IN PROBLEM
EOY CF
0 -$45,000.00
1$7,801.08
2$8,115.21
3$8,429.34
4$8,743.47
5$9,057.60
6$9,371.74
7$9,685.87
8$10,000.00
PW= $9,675.95 <–SOLVER TARGET CELL
=NPV(6%,CF YR 1:CF YR 8)-45000
NOW, SET UP ANOTHER TABLE OF CASH FLOWS USING THE FACT THAT
A8=$10,000, A1=$10,000-7*G, AND A0=-$45,000. THEN, USE SOLVER TO
FIND THE PW OF THE SERIES EQUAL TO THAT OF THE ORIGINAL SERIES
WHILE CHANGING THE VALUE OF G
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NOTE THAT THE INTEREST RATE FOUND USING SOLVER BELOW IS
THE SAME VALUE FOUND ABOVE.
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ANNUAL INCOMES, “A.” SELECT ANY VALUE FOR “A” IN THE CELL. IT
WILL LATER BE SET TO THE CORRECT VALUE.
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A B C D E F G H I
ANY INTEREST RATE FOR THE VALUE IN THE CELL. IT WILL LATER BE
SET TO THE CORRECT VALUE.
PROBLEM 2.93
an= 4
A0=-$10,000.00
A1=$3,000.00
G= $1,000.00
PW= $0.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
1$3,000.00
2$4,000.00
3$5,000.00
4$6,000.00
A= $4,226.00 <–SOLVER CHANGED CELL
P= $0.00 <–SOLVER TARGET CELL
FORMULAS
=-10000+A*((1+0.2489)^4-1)/(0.2489*(1+0.2489)^4)
THIS PROBLEM, IN WHICH THE VALUE OF THE INTEREST RATE IS TO
BE FOUND, IS BEST APPROACHED USING SOLVER. THIS IS DUE TO
OF THE INTEREST RATE. THEN, USE SOLVER TO SET THE PW VALUE
EQUAL TO 0 BY CHANGING THE INTEREST RATE i.
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A B C D E F G H I
A= $4,226.00 <–SOLVER CHANGED CELL
EOY CF
0 -$10,000.00
1$4,226.00
2$4,226.00
3$4,226.00
4$4,226.00
P= $0.00 <–SOLVER TARGET CELL
USING EXCEL’S NPV FUNCTION THIS IS
=NPV(24.8883%,4226,4226,4226,4226)-10000
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER.
NOTE THAT THE EQUAL ANNUAL INCOME “A” FOUND BELOW IS THE
SAME VALUE FOUND ABOVE.
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PROBLEM 2.94
i= 12.00%
n= 8
INITIAL CF= -$50,000.00
A1=$13,000.00
G= -$1,000.00
PW= $107.87 USING INTEREST TABLES THIS IS
=-$50,000+$13,000*(P|A 12%,8)-$1,000*(P|G 12%,8)
SEE BELOW FOR TABULATED CASH FLOWS TO CHECK ANSWER
EOY CF
0 -$50,000.00
1$13,000.00
2$12,000.00
3$11,000.00
4$10,000.00
5$9,000.00
6$8,000.00
7$7,000.00
8$6,000.00
PW= $107.87 USING EXCEL’S NPV FUNCTION THIS IS
=NPV(12%,CF YR 1:CF YR 8)-50000