Lecture_15._Interest_Rates_and_Rates_of_Return - 1 Interest...

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1 Interest Rates and Rates of Return A key problem in financial markets is to make instruments with different payment streams comparable. We do this via: Present Value Analysis : Comparing interest and principal directly in different periods is not appropriate because timing matters. $1 today is generally not the same as $1 tomorrow. x If we know the interest rate i , then the present value of $1 received n periods in the future is PV of $1 = $1/(1+i) n Remark : This shows immediately that bond prices and yield to maturity are inversely related. Discounting future payments at a higher rate reduces the present value of the bond’s future payments and therefore reduces the price of the bond today. x If we know the price and future payment schedule but not the interest rate, then we use the yield to maturity to calculate the interest rate for different credit instruments. The yield to maturity (i.e., current yield) is the interest rate i that equates the PV of a debt instrument with its current market value (i.e., price today). There are four main types of loans that are explained below. 1. Simple Loans : The borrower receives from the lender an amount called principal (P), and agrees to pay the principal plus an additional amount called interest (i), at a given maturity date. Example : Consider a 1-year simple loan with 10% interest. Repayment after 1 year is: Total Payment = P + iP = P(1+i) $11,000 = $10,000 + (0.10)($10,000) Solving for i, the yield to maturity is: i = [$11,000 - $10,000]/$10,000 = 10% Note: For a simple loan, the yield to maturity is the same as the simple interest rate. 2. Discount Bond : The borrower repays a specific face value (F) at maturity and receives a smaller price (D) initially known as the discount . Example
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Lecture_15._Interest_Rates_and_Rates_of_Return - 1 Interest...

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