1
05 Chapter model
121008
Chapter 5.
The Time Value of Money
Then, when you hit the enter key, you get the answer, 115.76.
Table 51.
Summary of Future Value Calculations
$100.00
5.00%
3
Periods:
0
1
2
3




Cash Flow Time Line:
$100
FV = ?
StepbyStep Approach:
$100
$105.00
$110.25
$115.76
=
$115.76
3
5
$100.00
$0
Calculator Approach:
N
I/YR
PV
PMT
FV
$115.76
Excel Approach:
Fixed inputs:
$115.76
Cell references:
$115.76
The Compounding Process: A Graphic View
You can work this problem in the same ways that we discussed above.
Table 52.
Summary of Present Value Calculations
$115.76
Interest rate
=
I
=
5.00%
No. of periods
=
N
=
3
Periods:
0
1
2
3




Cash Flow Time Line:
PV = ?
$115.76
StepbyStep Approach:
$100.00
$105.00
$110.25
$115.76
=
$100.00
3
5
$0
$115.76
Calculator Approach:
N
I/YR
PV
PMT
FV
$100.00
Excel Approach:
PV Function:
Fixed inputs:
$100.00
Cell references:
$100.00
In the Excel formula, 0 indicates that there are no intermediate cash flows.
The Discounting Process: A Graphic View
Present value (PV)
$100.00
Future value (FV)
$150.00
No. of years (N)
10
Interest rate function
= RATE(N,0,PV,FV)
Interest rate (I)
4 .14 %
=RATE(C111,0,C109,C110)
Present value (PV)
$500,000
Future value (FV)
$1,000,000
Interest rate (I)
4 .50%
No. of years (N)
=NPER(I,0,PV,FV)
No. of years (N)
15.74 73
=NPER(C122,0,C120,C121)
Table 53.
Summary:
Future Value of an Ordinary Annuity
Payment amount
= PMT =
$100.00
Interest rate
=
I
=
5.00%
3
Periods:
0
1
2
3




Cash Flow Time Line:
$100
$100
$100
$100.00
Multiply each payment by
$105.00
$110.25
$315.25
Formula Approach:
=
$315.25
3
5
$0
$100.00
Calculator Approach:
N
I/YR
PV
PMT
FV
$315.25
Excel Function Approach:
FV Function:
Fixed inputs:
$315.25
Cell references:
$315.25
Summary:
Future Value of an Annuity Due (Diagram Not in Text)
Payment amount
= PMT =
$100.00
Interest rate
=
I
=
5.00%
Number of periods
=
N
=
3
Periods:
0
1
2
3




Cash Flow Time Line:
$100
$100
$100
$105.00
Multiply each payment by
$110.25
$115.76
$331.01
Formula Approach:
=
$331.01
BEG MODE
3
5
0
100
Calculator Approach:
N
I
PV
PMT
FV
331.01
Excel Function Approach:
FV Function:
Fixed inputs:
331.01
Cell references:
331.01
Excel entries correspond with these calculator keys:
FV
Summary:
Present Value of an Ordinary Annuity
Payment amount
= PMT =
$100.00
Interest rate
=
I
=
5.00%
Number of periods
=
N
=
3
Periods:
0
1
2
3




Cash Flow Time Line:
$100
$100
$100
$95.24
Divide each payment by
$90.70
$86.38
$272.32
Formula Approach:
=
$272.32
3
5
100
0
Calculator Approach:
N
I
PV
PMT
FV
272.32
Excel Function Approach:
PV Function:
Fixed inputs:
272.32
Cell references:
272.32
Excel entries correspond with these calculator keys:
PV
Summary:
Present Value of an Annuity Due (Not in text; this is a "bonus")
Payment amount
= PMT =
$100.00
Interest rate
=
I
=
5.00%
Number of periods
=
N
=
3
Periods:
0
1
2
3




Cash Flow Time Line:
$100
$100
$100
$100.00
Divide each payment by
$95.24
$90.70
$285.94
Formula Approach:
=
$285.94
BEG MODE
3
5
100
0
Calculator Approach:
N
I
PV
PMT
FV
285.94
Excel Function Approach:
PV Function:
Fixed inputs:
285.94
Cell references:
285.94
Excel entries correspond with these calculator keys:
PV
FINDING PMT
No. of years (N)
5
Interest rate (I)
6%
Present value (PV)
$0
Future value (FV)
$10,000
END MODE
=PMT(I,N,PV,FV)
BEGIN MODE
=PMT(I,N,PV,FV,Type=1)
Payment (PMT )
$1,773.96
=PMT(C262,C261,C263,C264 )
Payment (PMT )
$1,673.55
FINDING N
Interest rate (I)
6%
Present value (PV)
$0
Payment (PMT)
$1,200
Future value (FV)
$10,000
=NPER(I,PMT,PV,FV)
No. of years (N)
6.96
=NPER(C274 ,C276,C275,C277)
FINDING I
No. of years (N)
5
Present value (PV)
$0
Payment (PMT)
$1,200
Future value (FV)
$10,000
=RATE(N,PMT,PV,FV)
Interest rate (I)
25.78%
=RATE(C284 ,C286,C285,C28
Would be tough to do!
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