McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
You hold an investment
for a period of
4 years .
Rates of return for each year are
4, 8, -10
and 9 respectively
. If you
invested 1000 at the beginning
of the term, how much will you
have at the end of the last year
?
- Future Value
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
1000
Year 1
Year 2
Year 3
Year 4
10 40
1 123.20
1 010.88
1000 1
+ .04
= 10
40 10
40 1 +
.08 =
1 123.20
= 1
010.88 =
1 101.86
1 123.20
1
-
.10 1
010.88 1 +
.09
…Alternative …Alternative
You hold an investment
for a period of
4 years .
Rates of return for each year are
4, 8, -10 and
9 respectively
. If you invested 1000 at the beginning
of the term,
how much will you have at the end of the last year ?
- Future Value
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
It is rare for interest to be compounded only once per year
It is rare for interest to be compounded only once per year
You hold an investment
for a period of
4 years .
Rates of return for each year are
4, 8, -10 and
9 respectively . If you
invested 1000 at the beginning
of the term, how much will you
have at the end of the last year
?
1000 1.
04 1.
08 .
90 1.
09 =
1 101.86
1 -10
Solving Alternative
Solving Alternative
Solve for all 4 years at
once Solve for all
4 years at once
- Future Value
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Compounding Frequencies and Periods
Frequency Frequency
No. per Year No. per Year
Period Period
Annually 1
1 year
Semiannually 2
6 months
Quarterly 4
3 months
Monthly 12
1 month
Daily 365
1 day
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Formula Formula
Development of a
n
Total Number
of
Periods Periods
Determining values for
n
and
i
Nominal or Annual
Rate j
Periodic
Rate per period
i
Number of compoundings per year
m
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Formulae Formulae
To Determine
n
To Determine
n
To Determine
i
To Determine
i
of Compounding Frequencies p.a. m
TimeYears
Annual
Interest Rate
j
of Compounding Frequencies p.a.
m
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
3
3
3
Annually
Semiannually
Quarterly
= 3 = 6
= 12
1 2
4
n n
Determining values for
n
If you compounded
100
for
3 years
at
6
annually ,
semiannually ,
or quarterly
, what are the values for n and
i ?
No. No.
of Compounding Frequencies per year
m
TimeYears Formula
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
If you compounded
100
for
3 years
at
6
annually ,
semiannually ,
or quarterly
, what are the values for n and
i ?
Determining values for
i
Rate - i Rate - i
6
6
6 1
2
4
= 6
= 3
= 1.5
Annually
Semiannually
Quarterly
Annual
Interest Rate
j of Compounding
Frequencies per year
m
Formula Formula
No. No.
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Formula Formula
Development of a for F
uture V
alue
PV =
Present Value Principal
i =
rate per period
n = number of periods FV
= PV
1 + i
n
Where…
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
FV =
PV 1 +
i
n
Formula Formula
Steve Smith deposited 1,000
in a savings account for 4 years
at a rate of 8
compounded semiannually .
What is Steve’s interest
and compo
unded amount?
Extract necessary data...
PV =
n =
i =
Solve…
- Future Value
4 X
2 =
8 1000
.08 2
= .04
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
FV =
PV 1 +
i
n
Formula Formula
Solve…
FV =
1000 1 +
.04
8
= 1000
1.368569 =
1 ,
368.57
Principal 1,000.00
+ Interest
368.57 Compo
unded 1
, 368.57
Using PV
= 1000
n = 8
i
= .04
- Future Value
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
BOTH ways will
be shown
BOTH ways will
be shown
Use a
calculator and
algebraic sequencing
Use the TI BAII Plus
financial calculator
There are
that can be used to
calculate compound interest:
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Solve… 1000
1 + .04
8
.04 1
8
1000
1,368.57 1
, 368.57
Use a
calculator and algebraic sequencing
Use a
calculator and algebraic sequencing
1368.57
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
8 8
Find the following KEYS: Find the following KEYS:
The Power function Key.
Used to calculate the value of exponents.
Used to access symbols located
“above” another key
, i.e. its acts like the
SHIFT key on a computer keyboard.
Use a
calculator and algebraic sequencing
Use a
calculator and algebraic sequencing
Changes the sign of the
data value of the number being displayed.
McGraw-Hill Ryerson©
Interest Compound
Interest
8 8
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