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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
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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