CHAPTER%204 - Measuring Interest Rates Yield on a Discount...

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Measuring Interest Rates Yield on a Discount Basis Interest Rates and Returns Real and Nominal Interest Rates Last Lecture: Money is everything generally accepted as payment Medium of exchange, unit of account, store of value Evolution of the payments system Monetary aggregates Money measures are linked to economic activity, inflation and interest rates
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Measuring Interest Rates Yield on a Discount Basis Interest Rates and Returns Real and Nominal Interest Rates CHAPTER 4 Understanding Interest Rates
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Measuring Interest Rates Yield on a Discount Basis Interest Rates and Returns Real and Nominal Interest Rates Present (Discounted) Value A dollar paid to you one year from now is less valuable than a dollar paid to you today. You can invest a dollar today and earn an interest rate in one year. Different debt instruments have very different streams of cash payments ( cash flows ). We can compare the value of these instruments by looking at their present value .
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Measuring Interest Rates Yield on a Discount Basis Interest Rates and Returns Real and Nominal Interest Rates Discounting the Future Consider a simple loan : lender provides the borrower with a amount of funds X (= principal ). The borrower repays (1 + i ) X at the maturity date . simple interest rate = interest payment principal = iX X = i Example: Suppose the annual simple interest rate is 10% and you lend out $100: Today 0 year 1 year 2 year n $100 (1 + 0 . 10) × $100 (1 + 0 . 10) × $110 ... (1 + 0 . 10) n × $100 = $110 = $121
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Measuring Interest Rates Yield on a Discount Basis Interest Rates and Returns Real and Nominal Interest Rates Simple Present Value Discounting the future : In the example, $121 after 2 years is worth $100 today. The present value ( PV ) is $100. PV = Cash Flow in year n (1 + i ) n = (1 + i ) n X (1 + i ) n = X The opportunity cost of holding $100 as cash rather than making the loan is: PV loan - PV cash = X - X (1 + i ) n = (1 + i ) n - 1 (1 + i ) n X
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Yield on a Discount Basis Interest Rates and Returns Real and Nominal Interest Rates Suppose you win a lottery paying you $1000 monthly for the next 20 years. The annual interest rate is 10%.
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CHAPTER%204 - Measuring Interest Rates Yield on a Discount...

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