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12 Certified Financial Controller CFC 6 Future Value
Single Deposit (Formula)
FV1 = P0 (1+i)1 = $1,000 (1.07)
= $1,070 Compound Interest
You earned $70 interest on your $1,000
deposit over the first year
deposit over the first year.
This is the same amount of interest you
would earn under simple interest.
13 Certified Financial Controller CFC Future Value
Single Deposit (Formula)
FV1 = P0 (1+i)1 FV2 = FV1 (1+i)1
= P0 (1+i)(1+i) = $1,000
000(1.07)(1.07)
= P0 (1+i)2
= $1,000(1.07)2
= $1,144.90
144. 14 = $1,000 (1.07)
= $1,070 You earned an EXTRA $4.90 in Year 2 with
compound over simple interest.
Certified
Certified Financial Controller CFC 7 General Future
Value Formula
FV1 = P0(1+i)1
FV2 = P0(1+i)2
etc. General Future Value Formula:
FVn = P0 (1+i)n
or FVn = P0 (FVIFi,n)  See Table I
FVIF 15 Certified Financial Controller CFC Valuation Using Table I
FVIFi,n is found on Table I
found on Table
at the end of the book. 16 Period
1
2
3
4
5 6%
1.060
1.124
1.191
1.262
1.338 7%
1.070
1.145
1.225
1.311
1.403 Certified Financial Controller CFC 8 8%
1.080
1.166
1.260
1.360
1.469 Using Future Value Tables
= $1,000 (FVIF7%,2)
= $1,000 (1.145)
= $1,145 [Due to Rounding]
Period
6%
7%
8%
1
1.060
1.070
1.080
2
1.124
1.145
1.166
3
1.191
1.225
1.260
4
1.262
1.311
1.360
5
1.338
1.403
1.469 FV2 17 Certified Financial Controller CFC Story Problem Example
Julie Miller wants to know how large her deposit
Miller wants to know how large her deposit
of $10,000 today will become at a compound
10,
annual interest rate of 10% for 5 years.
years 0 1 2 3 4 5 10%
$10,000
10, FV5
18 Certified Financial Controller CFC 9 Story Problem Solution
Calculation based on general formula:
based on general formula:
FVn = P0 (1+i)n
FV5 = $10,000 (1+ 0.10)5
= $16,105.10
16,105.
Calculation based on Table I:
FV5 = $10,000 (FVIF10%, 5)
FVIF
= $10,000 (1.611)
= $16,110 [Due to Rounding]
16,
19 Certified Financial Controller CFC Double Your Money!!!
Quick! How long does it take to
double $5,000 at a compound rate
of 12% per year (approx.)?
We will use the “Ruleof72”.
Ruleof 20 Certified Financial Controller CFC 10 The “Ruleof72”
“Ruleof72”
Quick! How long does it take to
double $5,000 at a compound rate
of 12% per year (approx.)? Approx. Years to Double = 72 / i%
Years to Double 72 i%
72 / 12% = 6 Years
Years
[Actual Time is 6.12 Years]
21 Certified Financial Controller CFC Present Value
Single Deposit (Graphic)
Assume that you need $1,000 in 2 years.
Let’s examine the process to determine
th
how much you need to deposit today at a
discount rate of 7% compounded annually. 0 7% 1 2 $1,000
PV0
22 PV1
Certified Financial Controller CFC 11 Present Value
Single Deposit (Formula)
PV0 = FV2 / (1+i)2
FV
= FV2 / (1+i)2
0 = $1,000 / (1.07)2
= $873.44
873.
1 7% 2 $1,000
PV0
23 Certified Financial Controller CFC General Present
Value Formula
PV0 = FV1 / (1+i)1
FV
PV0 = FV2 / (1+i)2
etc. General Present Value Formula:
Present Value Formula:
PV0 = FVn / (1+i)n
or
24 PV0 = FVn (PVIFi,n)  See Table II
PVIF
Certified Financial Controller CFC 12 Valuation Using Table II
PVIFi,n is found on Table II
found on Table II
at the end of the book.
Period
1
2
3
4
5
25 6%
.943
.890
.840
.792
.747 7%
.935
.873
.816
.763
.713 8%
.926
.857
.794
.735
.681 Certified
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This note was uploaded on 05/28/2013 for the course FINANCE economy taught by Professor Nill during the Fall '12 term at Bronx School Of Law And Finance.
 Fall '12
 nill
 Time Value Of Money

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