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Finding_the_Future_Value_of_Interest_Rates_060305

Finding_the_Future_Value_of_Interest_Rates_060305 - Finding...

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Saturday, June 04, 2005 13:34:10 1 Finding the Future Value of Interest Rates Geometric Mean Methodology 1. Assumption: Long Term Rates are based on a series of short term rates 2. The Present Value of a debt instrument is based on the expected value of short term interest rates in the future, i.e., 1 2 3 , 1,.., , (1 )(1 )(1 ) (1 ) t t FV PV i t r r r r = = + + + ⋅⋅⋅ + where r t equals the interest rate that will prevail in time t and FV t is the future value of the debt instrument in time t. t k Eq. 1
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Saturday, June 04, 2005 13:34:10 2 Example: Present Value of a $1000 Debt Instrument Year Expected Interest Rates 0 (today) 8% 1 10% 2 11% 3 11% FV t = $1000 PV 1 = $1000/(1.08) = $925.93 PV 2 = $1000/[(1.08)(1.10)] = $841.75 PV 3 = $1000/[(1.08)(1.10)(1.11)] = $758.33 PV 4 = $1000/[(1.08)(1.10)(1.11)(1.11)] = $638.18 Time to Maturity Present Value Yield to Maturity 1 $925.93 2 $841.75 3 $758.33 4 $638.18
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Saturday, June 04, 2005 13:34:10 3 Determining the Yield to Maturity Yield to maturity means that for a multiyear debt instrument you have to determine one interest rate for all years that is less than or equal to the expected short term interest rate for each year.
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