3.
Subtract the amount of the periodic payment available to reduce
the principal
from the unpaid balance at the beginning of the
period
, obtaining the “unpaid balance at the
end
of the period”.
4.
Equate the unpaid balance at the end of the period
to the unpaid
balance at the beginning of the
next
period.
5.
Repeat the process for subsequent periods.
36

PROBLEM 7: Loan Amortization
Schedule (Months 1 – 4)
37
↑ You Try
↑ You Try
↑ You Try
HOME LOAN AMORTIZATION SCHEDULE
Loan Amount
=
$500,000.00
Nominal Annual Interest Rate:
6.00%
Monthly Interest Rate =
0.500%
Months =
360
Payment Amount (round-up) =
$2,997.76
A
B
C
D
E
F
Month
Beginning Balance
Monthly Payment
Interest Amount
.
005*B
(Round-up)
Principal Reduction
C – D
Ending Balance
B – E
1
$500,000.00
$2,997.76
$2,500.00
$497.76
$499,502.24
2
$499,502.24
$2,997.76
$2,497.52
$500.24
$499,002.00
3
$499,002.00
$2,997.76
4
$2,997.76
↑ You Try
Check answers to problems
Appear at the end of this
document.

38
PROBLEM 8: Loan Amortization
Schedule (Months 358 – 360)
HOME LOAN AMORTIZATION SCHEDULE
Loan Amount
=
$500,000.00
Nominal Annual Interest Rate:
6.00%
Monthly Interest Rate =
0.500%
Months =
360
Payment Amount (round-up) =
$2,997.76
A
B
C
D
E
F
Month
Beginning Balance
Monthly Payment
Interest Amount
.
005*B
(Round-up)
Principal Reduction
C – D
Ending Balance
B – E
- - -
- - -
- - -
- - -
- - -
- - -
358
$8,901.60
$2,997.76
$44.51
$2,953.25
$5,948.35
359
$5,948.35
$2,997.76
360
1
4
2
3
0
↑ You Try
↑ You Try
↑ You Try
↑ You Try
Check answers to problems
Appear at the end of this
document.

The Effective Annual Interest Rate
(EAR)
DEFINITION
: The
E
ffective
A
nnual (Interest)
R
ate
(EAR),
associated with a nominal interest rate k
nom
, reports the
annual interest rate
(compounded one time a year)
that
yields the same FV as k
nom
, over the same length of time.
39

The EAR
–
Periodic Interest
PERIODIC INTEREST:
For a compounding frequency of m, the EAR
satisfies:
PV
(
∙
1 +
)
m
∙
t
=
PV
∙
(1 +
EAR
)
t
which, when solved for
EAR
, gives:
40
EAR
=
(
1 +
)
m
–
1

EXAMPLE:
EAR
–
Periodic Interest
PROBLEM 9:
Find the
EAR
associated with a 12%
nominal interest
rate compounded:
a.
Annually
b.
(
YOU TRY
) Semi-annually
Answer:
EAR
=
( 1 +
)
m
–
1
For a:
EAR
=
(
1 +
)
1
–
1
= .12
(
12%
)
For b (
YOU TRY
):
4
1
Check answers to problems
Appear at the end of this
document.

The EAR
–
Continuous Interest
CONTINUOUS INTEREST:
For a continuous annual
interest rate k
, the EAR satisfies:
PV
∙
e
k
∙
t
=
PV
∙
(1 + EAR)
t
which, when solved for EAR, gives:
42
EAR
=
e
k
–
1

EXAMPLE:
EAR
–
Continuous
Interest
PROBLEM 10 (
YOU TRY
):
Find the EAR associated with a
continuous annual interest rate of 12%?
ANSWER:
EAR
=
e
k
–
1
43
Check answers to problems
Appear at the end of this
document.

NOTES:
The EAR
NOTES:
THE “
TRUTH IN LENDING ACT”
(1969) requires that the EAR
appear on all lending agreements.
EAR provides a bench mark annual interest rate to which all other
interest rates may be compared. A higher EAR will assure a larger
accumulated amount
(net any extra charges).
EAR depends only on k
nom
(and m, for periodic interest)
-----
it does
not
depend on PV, t or FV
n
.

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