Chapter4 - Chapter 4 Solutions 2 You have just won \$10...

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Chapter 4 Solutions 2. You have just won \$10 million in the state lottery which promises to pay you \$1 million (tax free) every year for the next ten years. Have you really won \$10 million? No, because the present discounted value of these payments is necessarily less than \$10 million as long as the interest rate is greater than zero. 3. If the interest rate is 10%, what is the present value of a security that pays you \$1,100 next year, \$1,210 the year after, and \$1,331 the year after that? PV = FV 1 /(1+i) + FV 2 /(1+i) 2 + FV 3 /(1+i) 3 PV = \$1,100/1.1 + \$1,210/1.1 2 + \$1,331/1.1 3 = \$3,000 5. Write down the formula that is used to calculate the yield to maturity on a twenty-year 10% coupon bond with \$1,000 face value that sells for \$2,000. The present value is the purchase price of \$2,000. The future value is the face value of \$1,000. The annual coupon payment is 10% of the face-value, or \$100. The bond term is 20 years. The present value formula for a coupon bond is: PV = C/(1+i) + C/(1+i) 2 + … + C/(1+i) n + F/(1+i) n Plugging in the above information gives: \$2,000 = \$100/(1+i) + \$100/(1+i) 2 + … + \$100/(1+i) 20 + \$1000/(1+i) 20 Using a financial calculator, you could find the yield to maturity as i = 3%.

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