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A B C D E F G H
PROBLEM 2.59
i= 7.00%
n= 35
F= $2,000,000.00
A= $14,467.92 USING COMPOUND INTEREST FORMULAS THIS IS
=2000000*0.07/((1+0.07)^35-1)
A= $14,467.92 USING ELECTRONIC INTEREST TABLES THIS IS
=$2,000,000*(A|F 7%,35)
A= $14,467.92 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(0.07,35,,-2000000)
PROBLEM 2.60
i= 12.00%
n= 5
A= $1,000.00
A= $6,352.85 USING COMPOUND INTEREST FORMULAS THIS IS
=1000*((1+0.12)^5-1)/0.12
A= $6,352.85 USING ELECTRONIC INTEREST TABLES THIS IS
=$1,000*(F|A 7%,5)
A= $6,352.85 USING EXCEL’S FV FUNCTION THIS IS
=FV(0.12,5,,-1000)
PROBLEM 2.61
i= 7.00%
n= 5
P= $50,000.00
A= $12,194.53 USING COMPOUND INTEREST FORMULAS THIS IS
=50000*0.07*(1+0.07)^5/((1+0.07)^5-1)
A= $12,194.50 USING ELECTRONIC INTEREST TABLES THIS IS
=$2,000,000*(A|F 7%,35)
A= $12,194.53 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(0.07,5,-50000)
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A B C D E F G H
PROBLEM 2.62
i= 7.00%
n= 12
P= $200,000.00
WITH THE FIRST PAYMENT AT THE END OF YEAR 1
A= $25,180.40 USING COMPOUND INTEREST FORMULAS THIS IS
=200000*(0.07*(1+0.07)^12)/((1+0.07)^12-1)
A= $25,180.00 USING INTEREST TABLES THIS IS
=$200,000*(A|P 7%,12)
A= $25,180.40 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(0.07,12,-200000)
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A B C D E F G H I
PROBLEM 2.63
i= 5.00%
n= 10
A= $1,000.00
F= $12,577.89 USING COMPOUND INTEREST FORMULAS THIS IS
=7500*((1+0.04)^20-1)/0.04
F= $12,577.89 USING INTEREST TABLES THIS IS
=$1,000*(F|A 5%,10)
F= $12,577.89 USING EXCEL’S FV FUNCTION THIS IS
=FV(0.04,20,-7500)
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A B C D E F G H I
PROBLEM 2.64
a
P= $1.00
i= 7.000%
A= $0.20 20% OF P
n= 6.367 USING EXCEL’S NPER FUNCTION THIS IS
=NPER(7%,0.2,-1)
COULD ALSO USE SOLVER TO DETERMINE n
n= 6.367 <–SOLVER CHANGED CELL
P= $1.00 <–SOLVER TARGET CELL
USING EXCEL’S PV FUNCTION THIS IS
=PV(7%,n,-0.2)
bP= $1.00
n= 7
A= $0.20
i= 9.196% USING EXCEL’S RATE FUNCTION THIS IS
=RATE(7,0.2,-1)
COULD ALSO USE SOLVER TO DETERMINE i
i= 9.196% <–SOLVER CHANGED CELL
SINCE THE AMOUNT PAID IS NOT GIVEN, ANY AMOUNT WILL SERVE
TO ANSWER THE PROBLEM. A VALUE OF $1.00 IS SELECTED HERE
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A B C D E F G H I
PROBLEM 2.65
P= $6.00
n= 7
A= $1.00
i= 4.009% USING EXCEL’S RATE FUNCTION THIS IS
=RATE(7,0.2,-1)
COULD ALSO USE SOLVER TO DETERMINE i
i= 4.009% <–SOLVER CHANGED CELL
P= $6.00 <–SOLVER TARGET CELL
USING EXCEL’S PV FUNCTION THIS IS
=PV(i,7,-C6)
SINCE THE AMOUNT OF THE LOAN IS NOT GIVEN, ANY AMOUNT WILL SERVE TO
ANSWER THE PROBLEM. A VALUE OF $6.00 IS SELECTED HERE.
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NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME,
JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF
$10,000 10 YEARS LATER
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OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10
A B C D E F G H
OR, CAN DETERMINE THE FW OF THE CASH FLOW SERIES FROM YEARS 1-10
PROBLEM 2.66
ai= 6.00%
n= 10
A(1 TO 10)= $10,000.00
DISPLACED n= 10
A(11 TO 20)= $17,908.48 USING COMPOUND INTEREST FORMULAS THIS IS
=10000*(1+0.06)^10
A(11 TO 20)= $17,908.50 USING INTEREST TABLES THIS IS
=$10,000*(F|A 6%,10)*(A|P 6%,10)
A(11 TO 20)= $17,908.48 USING EXCEL’S PMT AND PV FUNCTIONS THIS IS
=PMT(6%,10,-FV(6%,10,,-PV(6%,10,-10000)))
=10000*(1+0.10)^10
A(11 TO 20)= $25,937.40 USING INTEREST TABLES THIS IS
=$10,000*(F|P 10%,10)
A(11 TO 20)= $25,937.42 USING EXCEL’S FV FUNCTION THIS IS
=FV(10%,10,,-10000)
NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME,
JUST DISPLACED 10 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF
$10,000 10 YEARS LATER
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3
4
5
6
7
8
9
10
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20
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NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME,
JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF
$10,000 TWO YEARS EARLIER
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OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10
A B C D E F G H
OR, CAN DETERMINE THE PW OF THE CASH FLOW SERIES FROM YEARS 3-10
PROBLEM 2.67
ai= 6.00%
n= 8
A(3 TO 10)= $10,000.00
DISPLACED n= 2
A(1 TO 8)= $8,899.96 USING COMPOUND INTEREST FORMULAS THIS IS
=10000/(1+0.06)^2
=$10,000*(P|A 6%,8)*(P|F 6%,2)*(A|P 6%,8)
A(1 TO 8)= $8,899.96 USING EXCEL’S PMT AND PV FUNCTIONS THIS IS
=PMT(6%,8,-PV(6%,2,,-PV(6%,8,-10000)))
=10000/(1+0.10)^2
A(1 TO 8)= $8,264.50 USING INTEREST TABLES THIS IS
=$10,000*(P|F 10%,2)
A(1 TO 8)= $8,264.46 USING EXCEL’S PV FUNCTION THIS IS
=PV(10%,2,,-10000)
NOTE THAT THESE CASH FLOWS ARE OVER THE SAME AMOUNT OF TIME,
JUST DISPLACED 2 YEARS. THEREFORE, SIMPLY DETERMINE THE WORTH OF
$10,000 TWO YEARS EARLIER
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A B C D E F G H
PROBLEM 2.68
i= 6.00%
P= $10,000.00 DEPOSIT AT EOY 0
A= -$1,000.00 WITHDRAWALS AT EOY 3-7
n1=10 YEARS FROM DEPOSIT TO FINAL WITHDRAWAL
n2=5 YEARS OF WITHDRAWALS (3, 4, 5, 6, 7)
n3=3 YEARS FROM 5TH WITHDRAWAL TO FINAL WITHDRAWAL
FIND THE FW AT EOY 10 OF THE INITIAL DEPOSIT AND THE FIVE WITHDRAWALS
F= $11,194.61 USING INTEREST TABLES THIS IS
=$10,000*(F|P 6%,10)-$1,000*(F|A 6%,5)*(F|P 6%,3)
F= $11,194.61 USING EXCEL’S FV FUNCTION THIS IS
=FV(6%,10,,-10000)+FV(6%,3,,-FV(6%,5,-(-1000)))
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A B C D E F G H
PROBLEM 2.69
i= 12.00%
n DEPOSITS= 30
A= $7,500.00 ($5,000 FROM YOU + $2,500 FROM EMPLOYER)
n WITHDRAWALS= 30
aF= $1,809,995.13 USING COMPOUND INTEREST FORMULAS THIS IS
=7500*(((1+0.12)^30-1)/0.12)
F= $1,809,995.10 USING INTEREST TABLES THIS IS
=$7,500*(F|A 12%,30)
F= $1,809,995.13 USING EXCEL’S FV FUNCTION THIS IS
=FV(12%,30,-7500)
b SUM(YOU)= $150,000.00 =5000*30
c SUM(EMPLOYER)= $75,000.00 =2500*30
d EARNINGS= $1,584,995.13 $1,584,995.13
e
A= $224,699.42 USING COMPOUND INTEREST FORMULAS THIS IS
=1809995.13*(0.12*(1+0.12)^30)/((1+0.12)^30-1)
A= $224,692.80 USING INTEREST TABLES THIS IS
=$1,809,995.13*(A|P 12%,30)
A= $224,699.42 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(12%,30,-1809995.13)
f FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWN
INTEREST ONLY= $217,199.42 =1809995.13*0.12
USING THE ANSWER TO PART a, FIND THE YEARLY AMOUNT OVER
THE WITHDRAWAL PERIOD
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A B C D
PROBLEM 2.70
aA= $2,000.00
i= 5.00%
n= 15
F= $43,157.13 USING COMPOUND INTEREST FORMULAS THIS IS
=2000*((1+0.05)^15-1)/0.05
F= $43,157.12 USING INTEREST TABLES THIS IS
=$2,000*(F|A 5%,15)
F= $43,157.13 USING EXCEL’S FV FUNCTION THIS IS
=FV(5%,15,-2000)
bA= $3,000.00
i= 8.00%
n(deposits=) 10
n(more years) 5
F= $63,856.54 USING COMPOUND INTEREST FORMULAS THIS IS
=3000*(((1+0.08)^10-1)/0.08)*(1+0.08)^5
F= $63,856.61 USING INTEREST TABLES THIS IS
=$3,000*(F|A 8%,10)*(F|P 8%,5)
F= $63,856.54 USING EXCEL’S FV FUNCTION THIS IS
=FV(8%,5,,-FV(8%,10,-3000))
=$2,000*(F|A 8%,5)*(F|P 8%,10)+$4,000*(F|A
8%,5)*(F|P 8%,5)+$6,000*(F|A 8%,5)
F= $95,010.55 EXCEL
=FV(8%,5,-6000)+FV(8%,5,,-FV(8%,5,-
4000))+FV(8%,5+5,,-FV(8%,5,-2000))
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i1=10.00%
n1=10
i2=5.00%
n2=3
FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF
THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE
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i1=9.00%
n1=5
i2=7.00%
n2=8
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A B C D E F
PROBLEM 2.71
aA= $4,000.00
i1=5.00%
n1=3
i2=8.00%
n2=5
F= $18,528.25 USING INTEREST TABLES THIS IS
=$4,000*(F|A 5%,3)*(F|P 8%,5)
F= $18,528.23 USING EXCEL’S FV FUNCTION THIS IS
=FV(8%,5,,-FV(5%,3,-4000))
bA= $12,000.00
F= $221,394.73 USING COMPOUND INTEREST FORMULAS THIS IS
=12000*(((1+10%)^10-1)/10%)*(1+5%)^3
F= $221,395.63 USING INTEREST TABLES THIS IS
=$12,000*(F|A 10%,10)*(F|P 5%,5)
F= $221,394.73 USING EXCEL’S FV FUNCTION THIS IS
=FV(5%,3,,-FV(10%,10,-12000))
cA= $18,000.00
F= $185,091.25 USING COMPOUND INTEREST FORMULAS THIS IS
=18000*(((1+9%)^5-1)/9%)*(1+7%)^8
F= $185,091.64 USING INTEREST TABLES THIS IS
=$18,000*(F|A 9%,5)*(F|P 7%,8)
FIRST, FIND THE FW OF THE ANNUAL DEPOSITS AS OF THE TIME OF
THE LAST SUCH DEPOSIT. THEN, FIND THE FW OF THAT SUM AT THE
NEW RATE FOR THE ADDITIONAL INVESTMENT PERIOD.
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A B C D E F G H I
PROBLEM 2.72
i= 9.00%
n1=25 NUMBER OF DEPOSITS
A= $4,000.00
t= 28 TIME OF FIRST WITHDRAWAL
n2=30 NUMBER OF WITHDRAWALS
a
F27= $402,532.54 USING COMPOUND INTEREST FORMULAS THIS IS
=4000*(((1+0.09)^25-1)/0.09)*(1+0.09)^2
F27= $402,532.56 USING INTEREST TABLES THIS IS
=$4,000*(F|A 9%,25)*(F|P 9%,2)
F27= $402,532.54 USING EXCEL’S FV FUNCTION THIS IS
=FV(9%,28-25-1,,-FV(9%,25,-4000))
b
A= $39,181.05 USING COMPOUND INTEREST FORMULAS THIS IS
=402532.54*(0.09*(1+0.09)^30)/((1+0.09)^30-1)
A= $39,182.52 USING INTEREST TABLES THIS IS
=$402,532.54*(A|P 9%,30)
A= $39,181.05 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(9%,30,-402532.54)
c
FOR THE ACCOUNT TO LAST FOREVER, ONLY THE INTEREST MAY BE WITHDRAWN
FIRST, DETERMINE THE AMOUNT IN THE ACCOUNT RIGHT AFTER THE LAST
DEPOSIT AT EOY 25. THEN, FIND THE FW OF THAT AMOUNT ONE YEAR
BEFORE THE FIRST WITHDRAWAL AT EOY 27
USING THE ANSWER TO PART a, FIND THE PAYMENT AMOUNT OVER THE
WITHDRAWAL PERIOD
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A B C D E F G H
PROBLEM 2.73
aA= $60,000.00
i= 10.00%
n(investment)= 19 1 YEAR BEFORE FIRST WITHDRAWAL
n(withdrawal)= 10 NUMBER OF WITHDRAWALS
P= $60,281.15 USING COMPOUND INTEREST FORMULAS THIS IS
=60000*((1+0.1)^10-1)/(0.1*(1+0.1)^10)*(1+0.1)^-19
P= $60,281.92 USING INTEREST TABLES THIS IS
$60,000*(P|A 10%,10)*(P|F 10%,19)
P= $60,281.15 USING EXCEL’S PV FUNCTION THIS IS
=PV(10%,20,,-PV(10%,10,-60000))
bA= $60,000.00
i= 15.00%
n(investment)= 19 1 YEAR BEFORE FIRST WITHDRAWAL
n(withdrawal)= 10 NUMBER OF WITHDRAWALS
P= $21,158.72 USING COMPOUND INTEREST FORMULAS THIS IS
=60000*((1+0.15)^10-1)/(0.15*(1+0.15)^10)*(1+0.15)^-19
P= $21,160.14 USING INTEREST TABLES THIS IS
$60,000*(P|A 15%,10)*(P|F 15%,19)
P= $21,158.72 USING EXCEL’S PV FUNCTION THIS IS
=PV(15%,20,,-PV(15%,10,-60000))
FIRST, FIND THE PW AT EOY 19 OF THE ANNUAL WITHDRAWALS. THEN, FIND
THE PW AT EOY 0.
FIRST, FIND THE PW AT EOY 19 OF THE ANNUAL WITHDRAWALS. THEN, FIND
THE PW AT EOY 0.
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A B C D E F G H I J K
PROBLEM 2.74
i= 10.00%
n= 8
EOY 0 1 2 3 4 5 6 7 8
CF -$2,500.00 $3,000.00 $4,500.00 $0.00 -$5,000.00 $0.00 -$1,000.00 $7,000.00 $3,000.00
P= $4,958.43 USING INTEREST TABLES THIS IS
A= $929.41 USING INTEREST TABLES THIS IS
=$4,958.43*(A|P 10%,8)
P= $4,958.37 USING EXCEL’S NPV FUNCTION THIS IS
=NPV(10%,3000,4500,0,-5000,0,-1000,7000,3000)-2500
A= $929.42 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(C3,C4,-C10)
=$2,500+$3,000*(P|F 10%,1)+$4,500*(P|F 10%,2)-$5,000*(P|F
10%,4)-$1,000*(P|F 10%,6)+$7,000*(P|F 10%,7)+$3,000*(P|F 10%,8)
FIRST, FIND THE PW OF THIS CASH FLOW SERIES. THEN FIND THE
EQUIVALENT VALUE OF “A”
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A B C D E F G H
PROBLEM 2.75
i= 12.00%
P= $15,000.00 LOAN VALUE AT EOY 0
A= $3,000.00 PAYMENTS AT EOY 1, 2, 3, 4
n1=4 YEARS UNTIL FINAL A=$3,000 PAYMENT
n2=1 ADDITIONAL YEARS UNTIL FINAL PAYMENT
F= $10,376.58 USING COMPOUND INTEREST FORMULAS THIS IS
=15000*(1+0.12)^(4+1)-(3000*(((1+0.12)^4-1)/0.12))*(1+0.12)^1
F= $10,376.55 USING INTEREST TABLES THIS IS
=$15,000*(F|P 12%,5)-$3,000*(F|A 12%,4)*(F|P 12%,1)
F= $10,376.58 USING EXCEL’S FV FUNCTION THIS IS
=FV(12%,4+1,,-15000)+FV(12%,1,,-FV(12%,4,3000))
F= $10,376.58 IS THE AMOUNT OF THE YEAR 5 PAYMENT
FIND THE LOAN VALUE AT EOY 5 AND SUBTRACT OFF THE PAYMENT
VALUES AT EOY 5. WHAT‘S LEFT IS THE FINAL LOAN PAYMENT AT EOY 5.
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6
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8
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22
NOW, DETERMINE THE VALUE AT EOY 40 OF THE THREE “$X” DEPOSITS
AT EOY 25, 30, AND 35 AND SOLVE FOR X
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45
46
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49
A B C D E
n4=10 YEARS FROM DEPOSIT 2 TO EOY 40
n5=5 YEARS FROM DEPOSIT 3 TO EOY 40
PROBLEM 2.76
i= 9.00%
n1= 10 YEARS OF WITHDRAWALS
n2=5 WITHDRAWALS REMAINING AT EOY 45
AMT45= $32,801.60 AMOUNT LEFT IN ACCT AT EOY 45
THE FOLLOWING WILL BE NEEDED IN THE LAST STEPS OF THE PROBLEM
n3=15 YEARS FROM DEPOSIT 1 TO EOY 40
AMT40= $54,120.41 USING INTEREST TABLES THIS IS
=$8433.04*(P|A 9%,10)
AMT40= $54,120.39 USING EXCEL’S PV FUNCTION THIS IS
=PV(9%,10,-8433.04)
AMT40= 7.54847 USING EXCEL’S FV FUNCTION THIS IS
TIMES X =(FV(9%,15,,-1)+(FV(9%,10,,-1)+(FV(9%,5,,-1)))) TIMES X
X= $7,169.72 =54120.39/7.54847
******************************************************
THIS PROBLEM MAY BETTER BE ANSWERED USING SOLVER
NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50
A= $8,433.05 =$54,120.84*(A|P 9%,10)
=$54,120.84*0.15582
NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45
AMT45= $32,801.60 <–SOLVER TARGET CELL
=$8,433.11*(P|A 9%,5)
NOW KNOWING THE ANNUAL WITHDRAWAL, DETERMINE THE AMOUNT
IN THE ACCOUNT AT EOY 40
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A B C D E
SOLVE FOR THE AMOUNT OF THE THREE DEPOSITS AT EOY 40
AMT40= $54,120.39 USING EXCEL’S FV FUNCTION THIS IS
=(FV(9%,15,,-X)+FV(9%,10,,-X)+(FV(9%,5,,-X))
NOW, SOLVE FOR THE ANNUAL WITHDRAWAL FROM EOY 41 TO 50
A= $8,433.04 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(9%,10,-54120.91)
NOW, SOLVE FOR THE AMOUNT REMAINING IN THE ACCOUNT AT EOY 45
AMT45= $32,801.60 <–SOLVER TARGET CELL
USING EXCEL’S PV FUNCTION THIS IS
=PV(9%,5,-8433.12)
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A B C D E F G
PROBLEM 2.77
P= $20,000.00 AT EOY 30
i= 5% YEARS 31-40
i= 6% YEARS 41-50
i= 7% YEARS 51 AND BEYOND
n1=10 YEARS AT 5%
n2=10 YEARS AT 6%
n3=10 YEARS AT 7%
n4=10 YEARS OF WITHDRAWALS
n5=5 YEARS OF WITHDRAWALS REMAINING AT EOY 65
a FIRST, SOLVE FOR THE AMOUNT AVAILABLE AT EOY 60
AMT60= $114,767.37 USING INTEREST TABLES THIS IS
=$20,000*(F|P 5%,10)*(F|P 6%,10)*(F|P 7%,10)
A= $16,340.58 USING INTEREST TABLES THIS IS
=$114,767.37*(A|P 7%,10)
AMT60= $114,767.63 USING EXCEL’S FV FUNCTION THIS IS
=FV(7%,10,,-FV(6%,10,,-FV(5%,10,,-20000)))
A= $16,340.33 USING EXCEL’S PMT FUNCTION THIS IS
=PMT(7%,10,-114767.63)
b
WDL65= $83,340.22 USING INTEREST TABLES THIS IS
=$16,340.58*(P|A 7%,5)+$16,340.58
WDL65= $83,338.90 USING EXCEL’S PV FUNCTION THIS IS
=PV(7%,5,-16340.33)+16340.33
SOLVE FOR THE PW OF THE 5 REMAINING WITHDRAWALS AT
EOY 66-70 PLUS THE WITHDRAWAL DUE AT EOY 65