FE PROBLEM 3.1
i = 8%
t CF(A) CF(B)
1$0 $5,000
2$0 $6,000
3$0 $7,000
4 X $8,000
FUTURE WORTH OF B = [$5,000 + $1,000(A|G 8%,4)](F|A 8%,4)
FUTURE WORTH OF B = [$5,000 + $1,000(1.40396)](4.50811) = $28,869.76
FUTURE WORTH OF A = X
TO BE EQUIVALENT, FW(A) = FW(B)
THEREFORE, X = $28,869.76
USING EXCEL
X =-FV(8%,4,,1000*NPV(8%,5,6,7,8))
X = $28,856.96
FE PROBLEM 3.2
i = 10%
t CF(A) CF(B)
1 X $5,000
2 X $4,000
3 X $3,000
4 X $2,000
5 X $1,000
ANSWER: d. $5,000(A|P 10%,5) – $1,000(A|G 10%,5)
rationale: RECOGNIZING THE CASH FLOWS AS A COMBINED UNIFORM SERIES
OF $5,000 AND A GRADIENT SERIES OF -$1,000
FE PROBLEM 3.3
THE ACCUMULATED INTEREST AT THE END OF YEAR 1 IS $500. THEREFORE, $1,510.57 IS A PRINCIPAL PAYMENT.
THE UNPAID BALANCE ON THE LOAN AFTER THE 1st PAYMENT IS $3,489.43. THEREFORE, THE ACCUMULATED
INTEREST AT THE END OF YEAR 2 IS $348.94. THE 2nd PAYMENT REDUCES THE UNPAID BALANCE ON THE
LOAN BY $1,661.63.
ANSWER: c
FE PROBLEM 3.4
IMMEDIATELY BEFORE MAKING THE FIRST PAYMENT, THE AMOUNT OWED ON THE LOAN IS
$10,000(F|P 15%,4) = $10,000(1.74901) = $17,490.10. THEREFORE, THE AMOUNT OF INTEREST
OWED ($7,490.10) IS GREATER THAN THE SIZE OF THE PAYMENT (6,661.08). HENCE, ALL OF
THE FIRST PAYMENT IS INTEREST. NO PRINCIPAL PAYMENT OCCURS IN THE FIRST
PAYMENT.
ANSWER: a
TO CALCULATE PAYMENT SIZE:
A = $10,000(F|P 15%,3)(A|P 15%,3)
A = $10,000(1.52088)(0.43798) = $6,661.15
A =PMT(15%,3,FV(15%,3,,10000))
A = $6,661.08
FE PROBLEM 3.5
FACE/PAR VALUE= $10,000.00
BOND RATE= 6.00% PER YEAR
PAYMENTS/YR= 2 SEMIANNUAL
SEMIANNUAL COUPON PAYMENTS = $10,000(0.06)/2 = $300
ANSWER: d
ASSUMING THE BOND IS REDEEMED AT FACE VALUE AFTER 2 YEARS, THE
SEMIANNUAL CASH FLOWS WILL BE: -$9,600, $300, $300, $300, $10,300
THE ANNUAL EFFECTIVE RETURN ON THE INVESTMENT WILL BE 1.032 – 1 =
0.0609 OR 6.09%, THEREFORE, THE BOND WILL EARN LESS THAN 10%.
FE PROBLEM 3.6
WORTH
EOY CF INTEREST @ EOY
0 -$1,000.00 -$1,000.00
1$3,000.00 6% $1,940.00 = -$1,000(1.06) + $3,000
2$2,000.00 8% $4,095.20 = $1,940(1.08) + $2,000
3$1,000.00 10% $5,504.72 = $4,095.20(1.10) + $1,000
ANSWER: b
FE PROBLEM 3.8
NOMINAL ANNUAL RATE 7.50%
MORTGAGE AMOUNT $162,000
MONTHLY PAYMENT $1,132.73
ACCUMULATED INTEREST $1,012.50 =162000*0.075/12
AFTER ONE MONTH
ANSWER: a
FE PROBLEM 3.9
ANNUAL WITHDRAWAL = $28,804.48 SOLVER CHANGE CELL
EOY CF
0 -$150,000.00
1$28,804.48
2$28,804.48
3$28,804.48
4$28,804.48
5$28,804.48
6$28,804.48
FW = $0.00 =(((((((C4*1.05+C5)*1.05+C6)*1.03+C7)*1.03)+C8)*1.04+C9)*1.04)+C10
ANSWER: c
PROBLEM 3.1
EOQ CF
0$7,000
1 -$600
2 -$600
3 -$600
4 -$600
5 -$1,500
6 -$1,500
7 -$1,500
8 -$1,500
QTR RATE = 3.515% =IRR(D5:D13)
EFFECTIVE ANNUAL INTEREST RATE = 14.817% =(1+D14)^4-1
ANSWER: 14.817%
PROBLEM 3.2
INTEREST RATE/QTR = 4%
EOQ CF
0
1 -$1,000
2 -$1,000
3 -$1,000
4 -$1,000
5 -$1,000
$1,000(F|A 4%,7)(F|P 4%,4) – $A(P|A 4%,4) = $0
A = $1,000(F|A 4%,7)(F|P 4%,4)(A|P 4%,4)
A = $1,000(7.89829)(1.16986)(0.27549)
A = $2,545.50
4 -$1,000
5 -$1,000
6 -$1,000
7 -$1,000
8$0
9$0
TWO SOLUTIONS ARE POSSIBLE, DEPENDING ON THE INTERPRETATION OF “A
QUARTERLY COMPOUNDING RATE OF 4%.”
14 $2,545
15 $2,545
PW = $0.00
INTEREST RATE/QTR = 1%
EOQ CF
0
1 -$1,000
2 -$1,000
3 -$1,000
4 -$1,000
5 -$1,000
6 -$1,000
7 -$1,000
8$0
9$0
10 $0
11 $0
12 $A
13 $A
14 $A
15 $A
$1,000(F|A 1%,7)(F|P 1%,4) – $A(P|A 1%,4) = $0
A = $1,000(F|A 1%,7)(F|P 1%,4)(A|P 1%,4)
EOQ CF
0$0
1 -$1,000
2 -$1,000
3 -$1,000
4 -$1,000
5 -$1,000
6 -$1,000
IF IT IS INTERPRETED THAT THE INTEREST RATE IS 4% PER ANNUM COMPOUNDED
QUARTERLY, THEN THE FOLLOWING SOLUTION RESULTS
11 $0
12 $1,924
13 $1,924
14 $1,924
15 $1,924
PW = $0.00
PROBLEM 3.3
INTEREST RATE = 6%
EOY CF
0 -$5,000.00
1$600.00
2$600.00
3$600.00
4$600.00
5$600.00
6$600.00
7$600.00
8$600.00
9$600.00
10 $600.00
11 $600.00
12 $1,600.00
AW = $600 + $1,000(A|F 6%,12) – $5,000(A|P 6%,12)
AW = $600 + $1,000(0.05928) – $5,000(0.11928)
AW = $62.88
EXCEL SOLUTION
AW =600-PMT(6%,12,-5000,1000)
AW = $62.89
PROBLEM 3.4
“PRICE” $7,000.00
TVOM i= 10.00% USED FOR PART a
TVOM i= 16.26% USED FOR PART b SOLVER CHANGED CELL
OPTION 1 OPTION 2
PAY= $6,500.00 NOW PAY DP= $1,000.00 NOW
i= 8.00%
m= 4
n= 2
PAY PMT= $819.06 QUARTERLY
a PW= $6,500.00 PW= $6,872.76 PREFER TO PAY CASH OF $6,500
b PW= $6,500.00 PW= $6,500.00 EXCEL SOLVER TARGET CELL
i= 16.26%
ieff=17.27%
PROBLEM 3.5
i= 6.50%
j= 8.00%
SERIES A
END OF YEAR 0 1 2 3 4 5
CASH FLOW $1,000.00 $1,080.00 $1,166.40 $1,259.71 $1,360.49
X= $1,162.01 SOLVER CHANGED CELL
SERIES B
END OF YEAR 0 1 2 3 4 5
CASH FLOW $1,162.01 $1,162.01 $1,162.01 $1,162.01 $1,162.01
a PW SERIES A $4,828.96
PW SERIES B $4,828.96 SOLVER TARGET CELL
b PW SER A (8%) $4,629.63 PREFER A AT 8%
PW SER B (8%) $4,639.59
c PW SER A (5%) $5,041.90
PW SER B (5%) $5,030.91 PREFER B AT 5%
PROBLEM 3.6
TVOM i= 14.00%
OPTION 1 A= $1,800.00
OPTION 2 Q= $656.97 SOLVER CHANGED CELL 1
OPTION 3 R= $1,511.34 SOLVER CHANGED CELL 2
END OF YEAR OPTION 1 OPTION 2 OPTION 3
0 $0.00 $0.00 $0.00
1 $1,800.00 $656.97 $1,511.34
2 $1,800.00 $1,313.93 $1,662.47
3 $1,800.00 $1,970.90 $1,828.72
4 $1,800.00 $2,627.86 $2,011.59
5 $1,800.00 $3,284.83 $2,212.75
PW $6,179.55 $6,179.55 SOLVER TARGET CELL 1 $6,179.55 SOLVER TARGET CELL 2
PROBLEM 3.7
TVOM i= 15.00%
SERIES A X= $908.52 SOLVER CHANGED CELL 1
SERIES B AS IN TABLE
SERIES C Y= $768.09 SOLVER CHANGED CELL 2
END OF YEAR SERIES A SERIES B SERIES C
0 -$1,000.00 -$2,500.00 $768.09
1 $908.52 $3,000.00 $768.09
2 $1,362.77 $2,500.00 $768.09
3 $1,817.03 $2,000.00 $1,536.17
4 $2,271.29 $1,500.00 $1,536.17
5 $2,725.55 $1,000.00 $1,536.17
PW $4,668.89 SOLVER TARGET CELL 1 $4,668.89 $4,668.89 SOLVER TARGET CELL 2
PROBLEM 3.8
TVOM i= 11.00%
SERIES A X= $798.12 SOLVER CHANGED CELL 1
SERIES B AS IN TABLE
SERIES C Y= $849.73 SOLVER CHANGED CELL 2
END OF YEAR SERIES A SERIES B SERIES C
0 $2,394.36 $1,000.00 $1,699.46
1 $1,995.30 $1,500.00 $1,699.46
2 $1,596.24 $2,000.00 $1,699.46
3 $1,197.18 $2,500.00 $849.73
4 $798.12 $3,000.00 $849.73
5 -$1,000.00 -$2,500.00 $849.73
PW $6,295.14 SOLVER TARGET CELL 1 $6,295.14 $6,295.14 SOLVER TARGET CELL 2
PROBLEM 3.9
TVOM i= 12.00%
SERIES 1 AS IN TABLE
SERIES 2 X= $12.77 SOLVER CHANGED CELL
END OF YEAR SERIES 1 SERIES 2
0 $150.00 $0.00
1 $200.00 $0.00
2 $250.00 $446.89
3 $300.00 $319.20
4 $0.00 $191.52
5 $0.00 $63.84
PW $741.40 $741.40 SOLVER TARGET CELL