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K. M. Bafna
IME, WMU
IME 3103
1 of 22
Interest and Equivalence
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Bafna, Professor, Western Michigan University.
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explicit written permission of Dr. Kailash M.
Bafna.
K. M. Bafna
IME, WMU
IME 3103
2 of 22
Interest and Equivalence
• Simple Interest vs. Compound Interest
• Repaying a Debt
• Equivalence
• Solution Methods
• Brief Review of Excel
• Single Payment Compound Interest
Formulas
• Single Payment Problems
K. M. Bafna
IME, WMU
IME 3103
3 of 22
Simple Interest vs. Compound Interest
Problem:
Deposit $100 now for a period of 5 years at an interest rate of 10% per
year.
How much do you get back at the end of 5 years using
(i) simple
interest
, and
(ii) compound interest
?
End of
Year
(EOY)
Accrued
Interest
Account
Balance
0
0
100
1
10
110
2
10
120
3
10
130
4
10
140
5
10
150
Simple Interest
NOTE:
In this course, we will only use COMPOUND
INTEREST unless mentioned otherwise.
Accrued
Interest
Account
Balance
0
100
Compound Interest
10.00
110.00
11.00
121.00
12.10
133.10
13.31
146.41
14.64
161.05
K. M. Bafna
IME, WMU
IME 3103
4 of 22
Repaying a Debt
Problem:
You borrowed $5,000 from your uncle to be paid off in 5
years at an annual interest rate of 8%.
The method of paying off
the loan is left up to you.
You find there are 4 ways that you can pay off the loan:
1.
At the end of each year, pay $1,000 plus accrued interest.
2.
At the end of each year, pay the accrued interest only and pay
the entire principal at the end of 5 years.
3.
Pay the entire principal and all accrued interest at the end of 5
years
(Note:
This is method 4 in textbook)
.
4.
Pay off all accrued interest and the principal in 5 equal annual
installments
(Note:
This is method 3 in textbook)
.
Which method should you select?
Let us analyze each of these methods.
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K. M. Bafna
IME, WMU
IME 3103
5 of 22
Repaying a Debt
1.
At the end of each year, pay $1,000 plus accrued interest.
Year
Amount
Owed at
Beginning of
Year
Accrued
Interest for
that Year
Total Owed
at End of
Year
Principal
Payment
Total endof
year
Payment
1
$5,000
$400
$5,400
$1,000
$1,400
5,000
1,400
1,320
1,240
1,160
1,080
1
2
3
4
5
yrs.
i = 8%/yr
2
4,000
320
4,320
$1,000
1,320
3
3,000
240
3,240
$1,000
1,240
4
2,000
160
2,160
$1,000
1,160
5
1,000
80
1,080
$1,000
1,080
$1,200
$5,000
$6,200
K. M. Bafna
IME, WMU
IME 3103
6 of 22
Repaying a Debt
2.
At the end of each year, pay the accrued interest only and pay the
entire principal at the end of 5 years.
Year
Amount
Owed at
Beginning
of Year
Accrued
Interest for
that Year
Total Owed at
End of Year
Principal
Payment
Total end
ofyear
Payment
1
$5,000
$400
$5,400
$0
$400
5,000
400
5,400
1
2
3
4
5
yrs.
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 Spring '07
 KailashBafna

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