Ch4 Lecture Notes

# Ch4 Lecture Notes - Nominal and Effective Interest Rates 1...

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1 Nominal and Effective Interest Rates

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3 Nominal Interest Rate q A nominal interest rate , r, is an interest rate that does not include any consideration of compounding q Mathematically we have the following definition: r = (interest rate per period)(No. of Periods)

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4 APR and APY q The terms APR and APY are used in many financial situations instead of nominal and effective interest rates. q The Annual Percentage Rate (APR) is the same as the nominal interest rate, and Annual Percentage Yield (APY) is used instead of effective interest rate.
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6 Example: Wachovia
7 Examples – Nominal Interest Rates q 1.5% per month for 24 months q Same as: (1.5%)(24) = 36% per 24 months q 1.5% per month for 12 months q Same as (1.5%)(12 months) = 18% / year q 1% per week for 1 year q Same as: (1%)(52 weeks) = 52% per year

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8 There are always 3 time based units associated with an interest rate statement. q Time period - the period over which the interest is expressed. This is the t in the statement of r % per time period t, for example, 1% per month. The time unit of 1 year is by far the most common. It is assumed when not stated otherwise. q Compounding period (CP) - the shortest time unit over which interest is charged or earned. This is defined by the compounding term in the interest rate statement, for example, 8% per year compounded monthly. If not stated, it is assumed to be 1 year. q Compounding frequency - the number of times that m compounding occurs within the time period t. If the compounding period CP and the time period t are the same, the compounding frequency is 1, for example, 1%
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10 10 4.5% per 6 months – compounded weekly q Nominal Rate: 4.5%. q Time Period: 6 months. q Compounded weekly: q Assume 52 weeks per year q 6-months then equal 52/2 = 26 weeks per 6 months q The effective weekly rate is: q (0.045/26) = 0.00173 = 0.173% per week
11 11 q The derivation of an effective interest rate formula directly parallels the logic used to develop the future worth relation: q The future worth F at the end of 1 year is the principal P plus the interest P ( i ) through the year. q Since interest may be compounded several times during the year, replace i with the effective annual rate i a and write the relation for F at the end of 1 year.

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12 12 The rate  per CP must be compounded through all  periods to obtain the total  effect of compounding by the end of the year.
13 13 Symbols used for nominal and effective interest rates

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## This note was uploaded on 04/07/2008 for the course MSE 304 taught by Professor Reiner during the Spring '08 term at CSU Northridge.

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Ch4 Lecture Notes - Nominal and Effective Interest Rates 1...

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