CHAPTER 5 PROBLEMS
THE TIME VALUE OF MONEY
PROBLEM 5-1
COMPOUND INTEREST
A)
Invest 5,000
Years 10
Percent 10%
FV =
B)
Invest 8,000
Years 7
Percent 8%
FV =
C)
Invest 775
Years 12
Percent 12%
FV =
D)
Invest 21,000
Years 5
Percent 5%
FV =
PROBLEM 5-2
COMPOUND VALUE SOLVING FOR N
A)
Invest 500
FV 1,039.50
Percent 5%
Page 1
N=
B)
Invest 35
FV 53.87
Percent 9%
N=
C)
Invest 100
FV 298.60
Percent 20%
N=
D)
Invest 53
FV 78.76
Percent 2%
N=
PROBLEM 5-3
COMPOUND VALUE SOLVING FOR I
A)
Invest 500
FV 1,948.00
Years 12
i=
B)
Invest 300
FV 422.10
Years 7
Page 2
i=
C)
Invest 50
FV 280.20
Years 20
i=
D)
Invest 200
FV 497.60
Years 5
i=
PROBLEM 5-4
PRESENT VALUE
A)
FV 800
Years 10
Percent 10%
PV =
B)
FV 300
Years 5
Percent 5%
PV =
C)
FV 1,000
Years 8
Percent 3%
PV =
D)
FV 1,000
Years 8
Percent 20%
PV =
Page 3
PROBLEM 5-5
COMPOUND ANNUITY
A)
Pymt 500
Years 10
Percent 5%
FV =
B)
Pymt 100
Years 5
Percent 10%
FV =
C)
Pymt 35
Years 7
Percent 7%
FV =
D)
Pymt 25
Years 3
Percent 2%
FV =
PROBLEM 5-6
PRESENT VALUE OF AN ANNUITY
A)
Invest 2,500
Years 10
Percent 7%
Page 4
PV =
B)
Invest 70
Years 3
Percent 3%
PV =
C)
Invest 280
Years 7
Percent 6%
PV =
D)
Invest 500
Years 10
Percent 10%
PV =
PROBLEM 5-7
COMPOUND VALUE
DATA
PV 10,000
Percent 6%
A)
1
5
15
B)
Percent 8% 10%
1
5
Page 5
15
PROBLEM 5-8
FUTURE VALUE
A)
FV 2,000,000
Years 35
Percent 4%
PV =
B)
FV 2,000,000
Years 35
Percent 14%
PV =
PROBLEM 5-9
COMPOUND INTEREST WITH NONANNUAL PERIODS
A)
PV 5,000
Years 5
Percent 6%
FV =
B)
Semiannual 2
Bimonthly 6
C)
Rate 12%
Annual
Semiannual
Page 6
Bimonthly
D)
Years 12
Annual
PROBLEM 5-10
SOLVING FOR I IN ANNUITIES
DATA
Rate = 11%
Annuity First Pymt Rec per Yr Years
A 50,000 8,500 12
B 60,000 7,000 25
C 70,000 8,000 20
PROBLEM 5-11
FUTURE VALUE
DATA
Copies 15,000
Percent 20%
Years' 3
FV for 1st yr =
FV for 2nd yr =
FV for 3rd yr =
PROBLEM 5-12
FUTURE VALUE
DATA
Percent 12%
Home runs 47
Years 5
FV for 1st yr =
Page 7
FV for 2nd yr =
FV for 3rd yr =
FV for 4th yr =
FV for 5th yr =
PROBLEM 5-13
LOAN AMORTIZATION
DATA
PV 80,000
Down payment 20,000
Years 25
Percents 9%
Pymts =
PROBLEM 5-14
SOLVING FOR A IN AN ANNUITY
DATA
FV 15,000
Years 15
Percent 6%
Pymts =
PROBLEM 5-15
SOLVING FOR I IN COMPOUND INTEREST
DATA
FV 1,079.50
PV 500
Years 10
Rate =
PROBLEM 5-16
PRESENT VALUE AND FUTURE VALUE OF AN ANNUITY
DATA
Years 10
Pv 100,000
Percent 5%
Page 8
FV =
Percent 10%
Pymt =
PROBLEM 5-17
COMPOUND VALUE
DATA
FV 10,000,000
Years 10
Percent 9%
Pymt =
PROBLEM 5-18
COMPOUND INTEREST WITH NONANNUAL PERIODS
Finance Co.
Percent 12%
Compound 12
Bank:
Percent 13%
Invest 1
Year 1
PROBLEM 5-19
PRESENT VALUE OF AN UNEVEN STREAM OF PAYMENTS
DATA
Percent 20%
Years A B C
1 10,000 10,000
2 10,000
3 10,000
4 10,000
5 10,000 10,000
6 10,000 50,000
7 10,000
8 10,000
9 10,000
10 10,000 10,000
Page 9
Total PV
PROBLEM 5-20
PRESENT VALUE
DATA
FV 1,000
Years 7
Percent 10%
PV =
PROBLEM 5-21
PERPETUITIES
A)
Perpetuity 300
Percent 8%
PV =
B)
Perpetuity 1,000
Percent 12%
PV =
C)
Perpetuity 100
Percent 9%
PV =
D)
Perpetuity 95
Percent 5%
PV =
PROBLEM 5-22
SOLVING FOR N WITH NONANNUAL PERIODS
DATA
Page 10
PV 1
Interest 16%
FV 4
Compound 2
Years 9
Semiannual Periods
PROBLEM 5-23
COMPLEX PRESENT VALUE
DATA
Annuity 10,000
Years 5
Beginning 10
Add pymt 20,000
Percent 6%
PV of 10,000 Annuity =
Step 1 (42,123.64)
Step 2 23,521.62
PV of Additional pymt = 8,345.30
Deposit Today
PROBLEM 5-24
LOAN AMORTIZATION
DATA
PV 50,000
Down payment 10,000
Installments 10
Percent 10%
Pymts =
PROBLEM 5-25
Page 11
SOLVING FOR I IN AN ANNUITY
DATA
PV 30,000
pymt 10,000
Installments 5
Percent =
PROBLEM 5-26
SOLVING FOR I IN COMPOUND INTEREST
DATA
PV 10,000
FV 27,027
Years 5
Interest =
PROBLEM 5-27
LOAN AMORTIZATION
DATA
PV 25,000
Percent 12%
Years 5
Pymts =
PROBLEM 5-28
PRESENT VALUE COMPARISON
Percent 11%
Years Amount PV
A Today 1,000
B 12 10,000
C 25 25,000
Page 12
PROBLEM 5-29
COMPOUND ANNUITY
DATA
Years 5
FV 20,000
Percent 12%
Pymt =
PROBLEM 5-30
COMPLEX PRESENT VALUE
DATA
FV 50,000
Years 15
Percent 7%
A)
Payment =
B)
PV =
C)
Deposit 10,000
years 10
FV =
Remaining balance=
Payment =
PROBLEM 5-31
COMPREHENSIVE PRESENT VALUE
DATA
Years 10
Savings 100,000
Stocks 300,000
Depositing:
Years 5
Page 13
Annuity 10,000
Years 5
Annuity 20,000
A)
Percent:
Savings 7%
Stocks 12%
1)
FV = 196,715.14
2)
FV = 931,754.46
3)
FV of dep = 138,164.48
4)
FV = 57,507.39
Total FV =
B)
Percent 10%
Years 20
Annuity =
PROBLEM 5-32
LOAN AMORTIZATION
DATA
No. of payments 20
Interest rate 15%
Amount borrowed 100,000
Annual Payments
PROBLEM 5-33
LOAN AMORTIZATION
Page 14
DATA
No. of payments 30
Interest rate 10%
Amount borrowed 150,000
Annual Payments
PROBLEM 5-34
PRESENT VALUE
DATA
Discount rate 10%
Amount per payment 50,000
No. of Payments without
current year's payment 19
Present value
DATA
Discount rate 20%
Amount per payment 50,000
No. of Payments without
current year's payment 19
Present value
PROBLEM 5-35
SOLVING FOR INTEREST IN COMPOUND INTEREST
Original Cost 0.12
This Problem cannot be solved by
No. of years lapsed 46 using the finance function in Excel.
Present Cost 22,000 The solution can be found by
Rate of return = 30.14% using Goal Seek.
PROBLEM 5-36
COMPREHENSIVE PRESENT VALUE
DATA
Beginning in year 5
Percent 10%
Annuity 50,000
Page 15
Years 19
Last fling 250,000
Years 20
Pass on 100,000
Years 25
PV of Annuity = 418,246.00
158,493.27
259,752.73
5,583.91
5,076.28
270,412.92
PV of Last fling = 37,160.91
PV of Pass On = 9,229.60
Total PV =
PROBLEM 5-37
SPREADSHEET PROBLEM
DATA
PV 900
Interest rate 8%
Payment 0%
Years 7
Future value =
PROBLEM 5-38
SPREADSHEET PROBLEM
DATA
PV 30,000
FV 250,000.00
Years 20
RATE =
PROBLEM 5-39
SPREADSHEET PROBLEM
DATA
PV 300,000
Monthly 12
Page 16
Years 25
Percent 8%
Pymts =
Period 48
Interest portion of payment
Principal portion of payment
PROBLEM 5-40
FUTURE AND PRESENT VALUE USING A CALCULATOR
DATA
A)
N 384
I/Y 6%
PV -24
PMT 0
CPT FV =
B)
N 4,608
I/Y 0.50%
PV -24
PMT 0
CPT FV =
C)
N 10
I/Y 10%
FV ($60,000,000,000)
PMT 0
CPT PV =
D)
N 10
PV (15,000,000,000)
PMT 0
FV 60,000,000,000
CPT I/Y =
E)
N 40
Page 17
I/Y 7%
PV (28,000,000,000)
FV 0
CPT PMT =
PROBLEM 5-41
COMPOUNDING USING A CALCULATOR
DATA
N 6
I/Y 3%
PV (15,000)
PMT 0
CPT FV
N 6
I/Y 7.5%
PMT 0
FV $17,910.78
CPT PV
PROBLEM 5-42
COMPOUNDING USING A CALCULATOR
DATA
N 45
I/Y 8.75%
PV 0
FV $1,000,000
CPT PMT
PROBLEM 5-43
COMPOUNDING USING A CALCULATOR
DATA
N 10
I/Y 20%
PMT $1,000,000,000
FV 0
CPT PV (4,192,472,085.55)
Page 18
N 20
I/Y 20%
PV 0
CPT PMT
PROBLEM 5-44
COMPOUNDING USING A CALCULATOR AND ANNUITIES DUE
DATA
N 25
I/Y 7.5%
PV (100,000)
PMT 0
CPT FV =
N 20
I/Y 7.5%
PV 0
PMT (1,500)
CPT FV = 64,957.02
TOTAL =
PROBLEM 5-45
NONANNUAL COMPOUNDING USING A CALCULATOR
DATA
N 60
I/Y 0.52%
PV (25,000)
FV 0
CPT PMT
PROBLEM 5-46
NONANNUAL COMPOUNDING USING A CALCULATOR
DATA
N 36
PV (999)
PMT 33
FV 0
Page 19
CPT I/Y = 0.97%
ANNUAL I/Y =
PROBLEM 5-47
NONANNUAL COMPOUNDING USING A CALCULATOR
DATA
N 60
I/Y 0.4%
PV (25,000)
FV 0
CPT PMT
N 60
I/Y 0.6%
PV (24,000)
FV 0
CPT PMT
PROBLEM 5-48
NONANNUAL COMPOUNDING USING A CALCULATOR
DATA
N 16
I/Y 1.6%
PV 0
PMT (1,000)
CPT FV =
PROBLEM 5-49
NONANNUAL COMPOUNDING USING A CALCULATOR
DATA
I/Y 1.1%
PV (5,000)
PMT 150
FV 0
CPT N =
PROBLEM 5-50
NONANNUAL COMPOUNDING USING A CALCULATOR
Page 20
DATA
A)
N 12
PV (160,000)
PMT 0
FV 420,000
CPT I/Y =
B)
N 10
PV (140,000)
PMT 0
FV 420,000
CPT I/Y =
C)
N 120
I/Y 0.5%
PV (140,000)
FV 420,000
CPT PMT
D)
N 120
PV (140,000)
PMT (500)
FV 420,000
CPT I/Y = 0.71%
ANNUAL I/Y =
PROBLEM 5-51
COMPLEX ANNUITY
DATA
N 140
I/Y 2.25%
PV 0
PMT (300)
CPT FV =
B)
N 60
Page 21
I/Y 2.25%
PV (20,000)
PMT 0
CPT FV =
TOTAL =
PROBLEM 5-52
SOLVING FOR I IN AN ANNUITY
DATA
N 20
PV (21,074)
PMT 3,000
FV 0
CPT I/Y =
PROBLEM 5-53
COMPLEX ANNUITY AND FUTURE VALUE
DATA
N 50
I/Y 6%
PMT 80,000
FV 0
CPT PV (1,260,949)
BOAT $300,000.00
N 43
I/Y 9.0%
PV 0
FV 1,560,949
CPT PMT
PROBLEM 5-54
FUTURE VALUE
DATA
N 200
I/Y 4%
PV (12,345)
Page 22
PMT 0
CPT FV
PROBLEM 5-55
SOLVING FOR r
DATA
N 7
PV (4,510)
PMT 0
FV 12,000
CPT I/Y
PROBLEM 5-56
SOLVING FOR N
DATA
I/Y 4.5%
PV (45,530)
PMT 0
FV 330,000
CPT N
PROBLEM 5-57
PRESENT VALUE
DATA
I/Y 7.0%
PMT 0
FV 398,930
N 28
CPT PV
MINI CASE
C)
1)
PV= 5,000
i= 8%
n= 10
FV=
2)
Page 23
FV= 1,671
PV= 400
i= 10%
n=
3)
FV= 4,046
PV= 1,000
n= 10
i=
D)
PV= 1,000
i= 10%
n= 5
FV=
F)
PMT= 1,000
i= 10%
n= 7
PV=
PV(a.d.)=
G)
PMT= 1,000
i= 10%
n= 7
FV=
FV(a.d.)=
H)
PV= 100,000
i= 10%
n= 25
PMT=
I)
PP= 1,000
i= 8%
PV=
J)
PMT= 1,000
i= 10%
n= 10
n= 9
PV= 6,144.57
K)
Page 24
PP= 1,000
i= 10%
n= 9
PV= 10,000.00
Page 25