LU 7
MATHEMATICS OF FINANCE
•
Simple Interest
•
Compound Interest
•
Annuities
•
Amortization and Sinking Funds
1

EXAMPLE 2:
TRUST FUNDS
•
An
amount
of
$2000
is
invested
in a
10
-year trust fund that pays
6%
annual
simple interest
.
•
What is the
total amount
of the trust
fund at the end of
10
years
?
2

EXAMPLE 2 SOLUTION:
TRUST
FUNDS
•
An
amount
of
$2000
is
invested
in a
10
-year trust fund that
pays
6%
annual
simple interest
.What is the
total amount
of
the trust fund at the end of
10
years
?
Solution
•
The
total amount
is given by
or
$3200
.
3
(1
)
2000[1
(0.06)(10)]
3200
A
P
rt

EXAMPLE 3 –
FUTURE VALUE AND PRESENT VALUE
An investor wants to have $20,000 in 9
months. If the best available interest rate
is 6.05% per year, how much must be
invested now to yield the desired
amount?
4

EXAMPLE 3 –
FUTURE VALUE AND PRESENT VALUE
An investor wants to have $20,000 in 9 months. If the best available
interest rate is 6.05% per year, how much must be invested now to yield
the desired amount?
S =
P +
I =
P +
Prt
.
•
5

EXAMPLE 5 –
PERIODIC COMPOUNDING
For each of the following investments, find the
interest rate per period,
i
, and the number of
compounding periods,
n
.
(a)
12% compounded monthly for 7 years
(b)
7.2% compounded quarterly for 11 quarters
6

EXAMPLE 5 –
PERIODIC COMPOUNDING
For each of the following investments, find the interest rate per
period,
i
, and the number of compounding periods,
n
.
(a)
12% compounded monthly for 7 years
If the compounding is monthly and
r
= 12% = 0.12, then
i
= 0.12/12 = 0.01.
The number of compounding periods is
n
= (7 yr)(12 periods/yr) = 84.
(b)
7.2% compounded quarterly for 11 quarters
i
= 0.072/4 = 0.018,
n
= 11 (the number of quarters given)
7

EXAMPLE 6 –
ANNUAL COMPOUNDING
If $3000 is invested for 4 years at 9% compounded
annually, how much interest is earned?
Solution:
The future value is
S
= $3000(1 + 0.09)
4
= $3000(1.4115816)
= $4234.7448
= $4234.74, to the nearest cent
8
Because $3000 of this amount was the original investment,
the interest earned is $4234.74
–
$3000 =
$1234.74
.

EXAMPLE
7
Find the total amount of RM10,000
after 5 years invested at a rate of
3% and compounded as followed:
(a)Annually
(b)Quarterly
(c)Semiannually
(d)Monthly
(e)Continuously
Which of the investments above
is the best?
9

EXAMPLE
7A
SOLUTION
P = RM10,000
n = 5 years
r = 3%
(a)Annually
10
5
)
1
(
5
03
.
0
1
03
.
0
nk
k
r
74
.
592
,
11
03
.
1
000
,
10
1
03
.
0
1
000
,
10
1
5
)
1
(
5
RM
S
k
r
P
S
nk
74
.
592
,
11
)
03
.
1
(
000
,
10
)
03
.
0
1
(
000
,
10
)
1
(
5
5
RM
S
S
S
r
P
S
n

EXAMPLE
7B
SOLUTION
P = RM10,000
n = 5 years
r = 3%
(b)Quarterly
11
20
)
4
(
5
0075
.
0
4
03
.
0
nk
k
r
84
.
611
,
11
0075
.
1
000
,
10
)
0075
.
0
1
(
000
,
10
)
1
(
20
20
RM
S
r
P
S
n

EXAMPLE
7C
SOLUTION
P = RM10,000
n = 5 years
r = 3%
(c)Semiannually
12
10
)
2
(
5
015
.
0
2
03
.
0
nk
k
r
41
.
605
,
11
015
.
1
000
,
10
)
015
.
0
1
(
000
,
10
)
1
(
10
10
RM
S
r
P
S
n

EXAMPLE
7D
SOLUTION
P = RM10,000
n = 5 years
r = 3%
(d)Monthly
13
60
)
12
(
5
0025
.
0

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