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F= $2.00
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A B C D E F G H I J K L M
PROBLEM 2.24
aP= $1.00
i= 6.00%
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR n
n=ln(F/P)/ln(1+i)
n= 11.90 =LN(2/1)/LN(1+0.06)
USE 12 YEARS
OR, CAN USE NPER EXCEL FUNCTION
P= $1.00
i= 6.00%
F= $2.00
n= 11.90 =NPER(6%,,-1.00,2.00)
USE 12 YEARS
OR, CAN USE SOLVER
P= $1.00
i= 6.00%
n= 11.90 <–SOLVER CHANGED CELL
USE 12 YEARS
F= $2.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$1.00*(1+0.06)^n
F= $2.00 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL’S FV FUNCTION THIS IS
=FV(6%,n,,-1.00)
bP= $1.00
i= 6.00%
F= $3.00
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR n
n=ln(F/P)/ln(1+i)
n= 18.85 =LN(3/1)/LN(1+0.06)
USE 19 YEARS
OR, CAN USE NPER EXCEL FUNCTION
P= $1.00
i= 6.00%
F= $3.00
n= 18.85 =NPER(6%,,-1.00,3.00)
USE 19 YEARS
OR, CAN USE SOLVER
P= $1.00
i= 6.00%
n= 18.85 <–SOLVER CHANGED CELL
USE 19 YEARS
F= $3.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$1.00*(1+0.06)^n
F= $3.00 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL’S FV FUNCTION THIS IS
=FV(6%,n,,-1.00)
cP= $1.00
i= 6.00%
F= $4.00
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR n
n=ln(F/P)/ln(1+i)
n= 23.79 =LN(4/1)/LN(1+0.06)
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A B C D E F G H I J K L M
USE 24 YEARS
OR, CAN USE NPER EXCEL FUNCTION
P= $1.00
i= 6.00%
F= $4.00
n= 23.79 =NPER(6%,,-1.00,4.00)
USE 24 YEARS
OR, CAN USE SOLVER
P= $1.00
i= 6.00%
n= 23.79 <–SOLVER CHANGED CELL
USE 24 YEARS
F= $4.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$1.00*(1+0.06)^n
F= $4.00 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL’S FV FUNCTION THIS IS
=FV(6%,n,,-1.00)
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F= $23,674.00
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A B C D E F G H I J K L M N
PROBLEM 2.25
aP= $10,000.00
n= 10
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR i
i=(F/P)^(1/n)-1
i= 9.0002% =(23674/10000)^(1/10)-1
OR, CAN USE RATE FUNCTION
P= $10,000.00
n= 10
F= $23,674.00
i= 9.0002% =RATE(10,,-10000,23674)
OR, CAN USE SOLVER
P= $10,000.00
n= 10
i= 9.0002% <–SOLVER CHANGED CELL
F= $23,674.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$10,000*(1+i)^10
F= $23,674.00 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL‘S FV FUNCTION THIS IS
=FV(i%,10,,-10000)
bP= $2,000.00
n= 18
F= $15,380.00
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR i
i=(F/P)^(1/n)-1
i= 12.0000% =(15380/2000)^(1/18)-1
OR, CAN USE RATE FUNCTION
P= $2,000.00
n= 18
F= $15,380.00
i= 12.0000% =RATE(18,,-2000,15380)
OR, CAN USE SOLVER
P= $2,000.00
n= 18
i= 12.0000% <–SOLVER CHANGED CELL
F= $15,380.00 <–SOLVER TARGET CELL
USING COMPOUND INTEREST FORMULAS THIS IS
=$2000*(1+i)^18
F= $15,380.00 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL‘S FV FUNCTION THIS IS
=FV(i%,18,,-2000)
cP= $2,500.00
n= 5
F= $4,212.00
USING COMPOUND INTEREST FORMULAS THIS IS
F=P*(1+i)^n
SOLVING FOR i
i=(F/P)^(1/n)-1
i= 10.9966% =(4212/2500)^(1/5)-1
OR, CAN USE RATE FUNCTION
P= $2,500.00
n= 5
F= $4,212.00
i= 10.9966% =RATE(5,,-2500,4212)
OR, CAN USE SOLVER
P= $2,500.00
n= 5
i= 10.9966% <–SOLVER CHANGED CELL
F= $4,212.00 <–SOLVER TARGET CELL
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A B C D E F G H I J K L M N
USING COMPOUND INTEREST FORMULAS THIS IS
=$2500*(1+i)^5
F= $4,212.00 COULD HAVE USED THIS AS SOLVER TARGET CELL
USING EXCEL‘S FV FUNCTION THIS IS
=FV(i%,5,,2500)
PROBLEM 2.26
F|P
i= 8.00%
n= 3
(F|P i%,n) = 1.25971 USING COMPOUND INTEREST FORMULAS THIS IS
=(1+0.08)^3
P|F
i= 10.00%
n= 20
(P|F i%,n) = 0.14864 USING COMPOUND INTEREST FORMULAS THIS IS
=1/(1+0.1)^20
CHECKS OK WITH APPENDIX A
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A B C D E F G
PROBLEM 2.27
i= 4.00%
n= 10
F= $100,000.00
P= $67,556.42 USING COMPOUND INTEREST FORMULAS THIS IS
=100000/(1+0.04)^10
P= $67,556.00 USING INTEREST TABLES THIS IS
=$100,000*(P|F 4%,10)
P= $67,556.42 USING EXCEL’S PV FUNCTION THIS IS
=PV(4%,10,,-100000)
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A B C D E F G H
PROBLEM 2.28
ai= 5.00%
n= 6
F= $10,000.00
P= $7,462.15 USING COMPOUND INTEREST FORMULAS THIS IS
=10000/(1+0.05)^6
P= $7,462.20 USING INTEREST TABLES THIS IS
=$10,000*(P|F 5%,6)
P= $7,462.15 USING EXCEL’S PV FUNCTION THIS IS
=PV(5%,6,,-10000)
bi= 8.00%
n= 4
F= $6,500.00
P= $4,777.69 USING COMPOUND INTEREST FORMULAS THIS IS
=6500/(1+0.08)^4
P= $4,777.70 USING INTEREST TABLES THIS IS
P= $1,689.70 USING INTEREST TABLES THIS IS
=$3,400*(P|F 6%,12)
P= $1,689.70 USING EXCEL’S PV FUNCTION THIS IS
=PV(6%,12,,-3400)
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A B C D E F G
PROBLEM 2.29
i= 5.00%
n= 25
F= $150,000.00
P= $44,295.42 USING COMPOUND INTEREST FORMULAS THIS IS
=150000/(1+0.05)^25
P= $44,295.00 USING INTEREST TABLES THIS IS
=$150,000*(P|F 5%,25)
P= $44,295.42 USING EXCEL’S PV FUNCTION THIS IS
=PV(5%,25,,-150000)
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A B C D E F G
PROBLEM 2.30
i= 11.00%
n= 9
F= $15,000.00
aP= $5,863.80 USING INTEREST TABLES THIS IS
=$15,000*(P|F 11%,9)
bP= $5,863.87 USING COMPOUND INTEREST FORMULAS THIS IS
=15000/(1+0.11)^9
cP= $5,863.87 USING EXCEL’S PV FUNCTION THIS IS
=PV(11%,9,,-15000)
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A B C D E F G H I
PROBLEM 2.31
i= 8.00%
CHOICE 1: TAKE TODAY
P= $1,000.00 ALREADY AT TIME 0
CHOICE 2: WAIT 3 YEARS AND TAKE
F= $1,500.00
n= 3
P= $1,190.75 USING COMPOUND INTEREST FORMULAS THIS IS
=1500/(1+0.08)^3
P= $1,190.75 USING INTEREST TABLES THIS IS
=$1,500*(P|F 8%,3)
P= $1,190.75 USING EXCEL’S PV FUNCTION THIS IS
=PV(8%,3,,-1500)
CHOICE 3: WAIT 5 YEARS AND TAKE
F= $3,000.00
n= 5
P= $2,041.75 USING COMPOUND INTEREST FORMULAS THIS IS
=3000/(1+0.08)^5
P= $2,041.74 USING INTEREST TABLES THIS IS
=$3,000*(P|F 8%,5)
P= $2,041.75 USING EXCEL’S PV FUNCTION THIS IS
=PV(8%,5,,-3000)
FOR EACH OF THE 3 CHOICES, DETERMINE THE VALUE AT THE SAME POINT
IN TIME. BELOW, THE POINT IN TIME WILL BE THE PRESENT (TIME 0)
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A B C D E F G H
PROBLEM 2.32
ai= 9.00%
n= 5
F= $19,000.00
P= $12,348.70 USING COMPOUND INTEREST FORMULAS THIS IS
=19000/(1+0.09)^5
P= $12,348.67 USING INTEREST TABLES THIS IS
P= $1,551.35 USING INTEREST TABLES THIS IS
=$8,300*(P|F 15%,12)
P= $1,551.33 USING EXCEL’S PV FUNCTION THIS IS
=PV(15%,12,,-8300)
di= 19.20%
n= 18
F= $13,000.00
P= $2,315.97 USING COMPOUND INTEREST FORMULAS THIS IS
=5000/(1+0.08)^10
P= $2,315.95 USING INTEREST TABLES THIS IS
=$5,000*(P|F 8%,10)
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A B C D E F G H
PROBLEM 2.33
i= 11.50%
n= 37
SET THE FUTURE WORTH AT $1.00
F= $1.00
THE (P|F 11.5%,37) FACTOR IS
P= 0.0178168 USING COMPOUND INTEREST FORMULAS THIS IS
=1/(1+0.115)^37
P= 0.0178168 USING EXCEL’S PV FUNCTION THIS IS
=PV(11.5%,37,,-1)
BOTH RESULTS ARE IDENTICAL
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A B C D E F G H
PROBLEM 2.34
i= 10.00%
n= 7
F= $23,384.61
TO FIND HOW MUCH HE BORROWED, FIND THE PW OF THE LOAN PAYOFF
P= $12,000.00 USING COMPOUND INTEREST FORMULAS THIS IS
=23384.61/(1+0.1)^7
P= $12,000.05 USING INTEREST TABLES THIS IS
=$23,384.61*(P|F 10%,7)
P= $12,000.00 USING EXCEL’S PV FUNCTION THIS IS
=PV(10%,7,,-23384.61)
PROBLEM 2.35
i= 10.00%
n= 12
F= $10,000.00
P= $3,186.30 USING INTEREST TABLES THIS IS
=$10,000*(P|F 10%,12)
P= $3,186.31 USING COMPOUND INTEREST FORMULAS THIS IS
=10000/(1+0.10)^12
P= $3,186.31 USING EXCEL’S PV FUNCTION THIS IS
=PV(10%,12,,-10000)
TO FIND THE EQUIVALENT SUM OF MONEY TODAY, FIND THE PW
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A B C D E F G H I
PROBLEM 2.36
i= 12.00%
n= 7
F= $6,000.00
aP= $2,714.10 USING INTEREST TABLES THIS IS
=$6,000*(P|F 12%,7)
bP= $2,714.10 USING COMPOUND INTEREST FORMULAS THIS IS
=6000/(1+0.12)^7
cP= $2,714.10 USING EXCEL’S PV FUNCTION THIS IS
=PV(12%,7,,-6000)
TO FIND THE SINGLE SUM OF MONEY DEPOSITED TODAY, FIND THE PW OF THE
WITHDRAWAL
PROBLEM 2.37
i= 12.00%
n= 10
F= $12,000.00
P= $3,863.64 USING INTEREST TABLES THIS IS
=$12,000*(P|F 12%,10)
P= $3,863.68 USING COMPOUND INTEREST FORMULAS THIS IS
=12000/(1+0.12)^10
P= $3,863.68 USING EXCEL’S PV FUNCTION THIS IS
=PV(12%,10,,-12000)
i= 6.00%
n= 10
F= $6,000.00
P= $3,350.34 USING INTEREST TABLES THIS IS
=$6,000*(P|F 6%,10)
P= $3,350.37 USING COMPOUND INTEREST FORMULAS THIS IS
=6000/(1+0.06)^10
P= $3,350.37 USING EXCEL’S PV FUNCTION THIS IS
=PV(6%,10,,-6000)
TO FIND THE SINGLE DEPOSIT NOW, FIND THE PW
TO FIND THE SINGLE DEPOSIT NOW, FIND THE PW
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A B C D E F G H I J
PROBLEM 2.38
i= 6.50%
n= 7
EOY 0 1 2 3 4 5 6 7
NCF $0.00 -$500.00 $200.00 $400.00 -$300.00 $500.00 -$200.00 $100.00
aF= $150.76 USING EXCEL’S FV FUNCTION THIS IS
$150.76 USING ELECTRONIC INTEREST TABLES THIS IS
bP= $97.02 USING EXCEL’S NPV FUNCTION THIS IS
=NPV(6.5%,-500,200,400,-300,500,-200,100)+0
$97.02 USING ELECTRONIC INTEREST TABLES THIS IS
cP= $97.02 CONVERTING THE FW TO PW USING EXCEL’S PV FUNCTION
=PV(6.5%,7,,-150.76)
$97.02 USING ELECTRONIC INTEREST TABLES THIS IS
=$150.76*(P|F 6.5%,7)
=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*(P|F 6.5%,1)+$200*(P|F 6.5%,2)+$400*(P|F 6.5%,3)-
$300*(P|F 6.5%,4)+$500*(P|F 6.5%,5)-$200*(P|F
6.5%,6)+$100*(P|F 6.5%,7)
=-$500*(F|P 6.5%,6)+$200*(F|P 6.5%,5)+$400*(F|P 6.5%,4)-
300*(F|P 6.5%,3)+500*(F|P 6.5%,2)-200*(F|P 6.5%,1)+100
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A B C D E F G H I J K
PROBLEM 2.39
i= 7.00% COMPOUNDED ANNUALLY
n= 11
EOY 0 1 2 3 4 5 6 7 8
DEP/WDL $2,000.00 $0.00 $0.00 -$1,000.00 $0.00 $3,000.00 $0.00 $0.00 $1,500.00
FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11
F= $8,831.27 USING COMPOUND INTEREST FORMULAS THIS IS
FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11
F= $8,831.26 USING INTEREST TABLES THIS IS
FIND THE FW OF EACH DEPOSIT OR WITHDRAWAL AT YEAR 11
F= $8,831.27 USING EXCEL’S FV FUNCTION THIS IS
SUM THE PW OF EACH DEPOSIT OR WITHDRAWAL AND THEN FIND ITS FW
F= $8,831.27 USING EXCEL’S FV AND NPV FUNCTIONS THIS IS
=FV(7%,11,,-(NPV(7%,0,0,-1000,0,3000,0,0,1500)+2000))
=2000*(1+0.07)^11-
1000*(1+0.07)^8+3000*(1+0.07)^6+1500*(1+0.07)^3
=$2,000*(F|P 7%,11)-$1,000*(F|P 7%,8)+$3,000*(F|P
7%,6)+$1,500*(F|P 7%,3)
=FV(7%,11,,-2000)+FV(7%,8,,1000)+FV(7%,6,,-
3000)+FV(7%,3,,-1500)
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A B C D E F G H I J K
PROBLEM 2.40
i= 8.00%
n= 8
EOY 0 1 2 3 4 5 6 7 8
NCF $300.00 $300.00 $600.00 -$500.00 –$300.00 $0.00 $800.00 $700.00 $600.00
aP= $1,711.50 USING EXCEL’S NPV FUNCTION THIS IS
=NPV(8%,300,600,-500,-300,0,800,700,600)+300
$1,711.50 USING INTEREST TABLES THIS IS
bF= $3,167.86 USING EXCEL’S FV FUNCTION THIS IS
=FV(8%,C4,,-C9)
F= $3,167.86 USING INTEREST TABLES THIS IS
=$1,711.50*(F|P 8%,8)
c F2= $1,996.29 USING EXCEL’S FV FUNCTION THIS IS
=FV(8%,2,,-1711.5)
F2= $1,996.29 USING INTEREST TABLES THIS IS
=$1,711.50*(F|P 8%,2)
=$300+$300*(P|F 8%,1)+$600*(P|F 8%,2)-$500*(P|F 8%,3)-$300*(P|F
8%,4)+$800*(P|F 8%,6)+$700*(P|F 8%,7)+$600*(P|F 8%,8)
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A B C D E
PROBLEM 2.41
i= 7.50% COMPOUNDED ANNUALLY
n= 10
EOY DEPOSIT
0$5,000.00
1$1,000.00
2$1,000.00
FIND THE FW OF EACH DEPOSIT AT YEAR 10
F= $14,005.87 USING COMPOUND INTEREST FORMULAS THIS IS
=5000*(1+0.075)^10+1000*(1+0.075)^9+1000*(1+0.075)^8
FIND THE FW OF EACH DEPOSIT AT YEAR 10
F= $14,005.87 USING ELECTRONIC INTEREST TABLES THIS IS
=$5,000*(F|P 7.5%,10)+$1,000*(F|P 7.5%,9)+$1,000*(F|P 7.5%,8)
FIND THE FW OF EACH DEPOSIT AT YEAR 10
F= $14,005.87 USING EXCEL’S FV FUNCTION THIS IS
=FV(7.5%,10,,-5000)+FV(7.5%,9,,-1000)+FV(7.5%,8,,-1000)
SUM THE PW OF EACH DEPOSIT AND THEN FIND ITS FW
F= $14,005.87 USING EXCEL’S FV AND NPV FUNCTIONS THIS IS
=FV(7.5%,10,,-(NPV(7.5%,1000,1000)+5000))