McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
If you compounded
100
for
3 years
at
6
annually, semi
annually, or quarterly
, what are the final amounts that you would have at
the end of the three 3 years
?
- Future Value
Annual Annual
FV
A
= 100
1. 06
3
119.10 1
19 .
10
Semi- Semi-
FV
S
= 100
1. 03
6
119.41 1
19 .
41
Semi = 6
2
Quarterly Quarterly
FV
Q
= 100
1. 015
12
119.56 1
19 .
56
Quarterly = 6
4
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
F u
tu re
V al
u e
S
o r
F V
F u
tu re
V al
u e
S
o r
F V
1 2
3 4
5 6
7 8
9 10
11
50 100
150 200
250
FV =
PV 1+
i
n
TimeYears
S= P
1+ r
t
Original Principal Original Principal
Interest on
Original Principal
Interest on
Interest
- Future Value
The Components of the Future Value of 100
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Comparisons Comparisons
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Al Jones deposited 1,000 in a savings account for 5 years at 10 p.a..
Al Jones deposited 1,000 in a savings account for 5 years at 10 p.a..
Annual
S
imple
I
nterest Rate of 10
Annual
S
imple
I
nterest Rate of 10
Annual
C
ompound Rate of 10
Annual
C
ompound Rate of 10
Interest
What is Al’s
S
imple
I
nterest and
M
aturity
V
alue? What is Al’s
S
imple
I
nterest and
M
aturity
V
alue? What is Al’s
I
nterest and
C
ompounded
V
alue? What is Al’s
I
nterest and
C
ompounded
V
alue?
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Interest
FV =
PV 1 +
i
n
Formulae Formulae
I =
P r
t
I
= 1,000
.10 5
= 500
FV =
1,000 +
500
=
1 ,
500 FV
= 1000
1. 1
5
= 1,000
1.6105
=
1 ,
610.51 n
= 5
1
=
5
I
= FV
–
PV =
1 610.51
- 1000
Simple Simple
Compound Compound
Al Jones deposited 1,000 in a savings account for 5 years at 10 Al Jones deposited 1,000 in a savings account for 5 years at 10
= 610.51
i =
.10
Compare
Compare
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
200 400
600 800
1000 1200
1400 1600
1800
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
17 18
19 20
21 22
23 24
25 26
Years to Maturity ,
n
Future Values of
100
at
Various Rates of Interest Compounded
Annually
F uture
V alues of
100
at
Various Rates of Interest Compounded
Annually
100
6 10
8 12
F u
tu re
V al
u e
F V
F u
tu re
V al
u e
F V
Interest Compound
Interest
8 8
8 8
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Ending Balance
Ending Balance
Compounding Period
Compounding Period
1,000 1,000
Nominal Rates
of Interest
Compared
1 ,
060.00
1 ,
060.90
1 ,
061.36
1 ,
061.83
Beginning Balance
Beginning Balance
Nominal Rate
Nominal Rate
+ 6 + 6
Annual
Semiannual
Quarterly
Daily
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
500 1000
1500 2000
2500
5 10
15 20
25
F u
tu re
V al
u e
F V
F u
tu re
V al
u e
F V
Time years
12 Compounded
monthly
F uture
V alues of
100
at the same Nominal
Rate b
ut
Different Compounding Frequencies
12 Co
mp oun
ded
An nua
lly
Interest Compound
Interest
8 8
8 8
100
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Calculate the
F uture
V alue
of
2,000
compounded
daily
for
4 years
at
4.5.
n
=
i
=
=
2,000 1.1972 =
2,394.41
=
2,000 1.1972 =
2 ,
394.41
FV =
2000 1+
.045 365
1460
FV =
PV 1 +
i
n
Formula Formula
Compounding Compounding
Daily Daily
Interest Interest
Compounding Compounding
Daily Daily
Interest Interest
Interest Compound
Interest
8 8
8 8
4
365 =
1460
. 045
365 = 0.0001232
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
2394.41 .045
365 1
1460
2000 Solve
FV =
2000 1+
.045 365
1460
= 2,394.41 =
2 ,
394 .
41 Compounding
Compounding Daily
Daily Interest
Interest Compounding
Compounding Daily
Daily Interest
Interest
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
FV
=
- 2394.41
4.5
2000
2,394.41 2
, 394
. 41
Set the frequency
of interest
compounding Set the
frequency of
interest compounding
Step 1 Step 1
4 365
Input values into the
financial keys Input values
into the financial keys
Step 2 Step 2
Compounding Compounding
Daily Daily
Interest Interest
Compounding Compounding
Daily Daily
Interest Interest
365
Calculate the Future Value
of 2,000
compounded daily for 4
years at 4.5. Calculate the
F uture
V alue
of 2,000
compounded daily for
4 years
at 4.5.
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
You invested 6000
at 4.5
compounded quarterly .
After 2 years
, the rate changed to 5.2
compounded monthly .
What amount will you have 4
1
2 years after the initial
investment?
Prepare a ‘time-line’ as part of the solution
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
You invested 6000
at 4.5
compounded quarterly .
After 2 years
, the rate changed to 5.2
compounded monthly .
What amount will you have 4
1
2
years after the
initial investment?
2 years 4.5 years
6000 i
= .045
4 FV
1
= PV
2
FV
1
= 6000
1+ .045
4
8
= 6000
1.0936 =
6 561.75
FV
2
i = .
052 12
FV
2
= = 6561.751.1385
= 7470.61
6 561.75
1+. 052
12
30
n = 2
4 = 8
n = 2.5
12 = 30
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
You invested 6000
at 4.5
compounded quarterly
. After
2 years ,
the rate
changed to 5.2
compounded monthly
. What amount
will you have 4
1
2
years after
the initial investment?
6000
Set the frequency
of interest
compounding Set the
frequency of
interest compounding
Step 1 Step 1
4 2
4.5
Input values into the
financial keys
Input values
into the financial
keys
Step 2 Step 2
6,561.75 6
, 561.75
Using the TI BAII Plus financial calculator Using
the TI BAII Plus
financial calculator
FV
1
= PV
2
FV
1
= PV
2
FV
2
4 6,571.75
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
You invested 6000
at 4.5
compounded quarterly
. After
2 years ,
the rate
changed to 5.2
compounded monthly
. What amount
will you have 4
1
2
years after
the initial investment?
7470.61
Set the frequency
of interest
compounding Set the
frequency of
interest compounding
Step 1 Step 1
2.5 12