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# 3 - Interest and Equivalence Interest and Equivalence...

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1 K. M. Bafna IME, WMU IME 310-3 1 of 22 Interest and Equivalence WARNING The Power Point slide presentation following this slide is copyrighted by Dr. Kailash M. Bafna, Professor, Western Michigan University. This entire presentation or any parts thereof may not be used for any purpose without the explicit written permission of Dr. Kailash M. Bafna. K. M. Bafna IME, WMU IME 310-3 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 310-3 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 310-3 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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2 K. M. Bafna IME, WMU IME 310-3 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 end-of- 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 310-3 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- of-year Payment 1 \$5,000 \$400 \$5,400 \$0 \$400 5,000 400 5,400 1 2 3 4 5 yrs.
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