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Lesson+9+Understanding+Interest+Rates

# Lesson+9+Understanding+Interest+Rates - Lesson 9...

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Lesson 9: Understanding Interest Rates M&B Chapter 4, 5

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Would you rather have \$100 today or \$105 in one year? What does your answer depend on? What happens to your choice as the interest rate rises? As the interest rate falls? Present value is the amount of money you would need to invest today to yield a given future return. The Present Value of One Future Payment
Present value is based in two ideas 1. You can determine how much money you have available at different times 2. Interest is earned on past interest (compounding) Present Value (cont’d)

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Compare \$300 today vs. \$350 in two years What does it depend on? Today, your principal ( P ) represents your entire investment What rate of interest will you earn? In one year : (1 + i ) × P Where i is annual interest rate In two years : (1 + i ) 2 × P Compounding is earning interest on interest that was earned in prior years The Power of Compounding
Concept of “Present Value” A dollar paid to you one year from now is less valuable than a dollar paid to you today

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How Much Would \$100 Invested At 10% Be Worth in the Future (Future Value)---\$100 X (1.10)^n \$100 invested at 10% \$100.00 1.10 \$110.00 after 1 years \$110.00 1.10 \$121.00 " 2 " \$121.00 1.10 \$133.10 " 3 " \$133.10 1.10 \$146.41 " 4 " \$146.41 1.10 \$161.05 " 5 " \$161.05 1.10 \$177.16 " 6 " \$177.16 1.10 \$194.87 " 7 " \$194.87 1.10 \$214.36 " 8 " \$214.36 1.10 \$235.79 " 9 " \$235.79 1.10 \$259.37 " 10 " \$259.37 1.10 \$285.31 " 11 " \$285.31 1.10 \$313.84 " 12 " \$313.84 1.10 \$345.23 " 13 " \$345.23 1.10 \$379.75 " 14 " \$379.75 1.10 \$417.72 " 15 " \$417.72 1.10 \$459.50 " 16 "
Extend as many years as you would like Value after N years = (1 + i ) N × P Compounding enables your money to keep working for you, even without additions to the principal Compounding

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Compounding makes a huge difference Compounding P = \$1,000, i = 8% 1 year: \$1,080 5 years: \$1,469 10 years: \$2,159 25 years: \$46,902 100 years: \$2,199,761
How much does the interest rate matter? Compounding (cont’d) \$1,000 × 1.08 100 = \$2,199,761 \$1,000 × 1.07 100 = \$867,716 1% makes a BIG difference!!!

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In discounting, we consider an amount to be received in the future and ask how much it is worth today. Example : Would you rather have \$350 in one year, or \$300 today?
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Lesson+9+Understanding+Interest+Rates - Lesson 9...

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