Nominal%20and%20Effective%20Interest%20Rates

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Chapter 4

• Nominal and Effective Interest Rates

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Nominal Interest Rate

• Is an interest rate that does not include any
  consideration of compounding.
• It is represented by r.
• r (interest rate per period) (Number
• of periods)
• r per time period t

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Example

• For an interest rate of 0.50 per month,
  determine the nominal interest rate per
• (a) quarter
• (b) year
• (c) 2 years

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Solution

• a) r (0.50 )(3) 1.5
• b) r (0.50 )(12)6
• c) r (0.50 )(24)12

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Effective Interest Rate

• Is the actual interest rate that applies for a
  stated period of time. It is commonly expressed
  in an annual basis.
• 12 per year, compounding monthly
• r per time period t, compounding m-ly

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Effective Interest rate

• To obtain the effective interest rate per
  compounding period, you need to divide the
  interest rate per time period over number of
  compounding frequency.
• Effective rate per CP (r per time period t) /
  (m compounding periods per t)
• i r/m

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Example

• For an interest rate of 18 per year compounded
  monthly, determine the nominal interest rate per
• (a) 2 months
• (b) 6 months
• (c) 2 years.

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Solution

• imonthly 18 / 12
• 1.5
• a) (1.5) / 2 3
• b) (1.5) / 6 9
• c) (1.5) / (24) 36

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Effective Annual Interest Rates

• r Nominal interest rate per year
• m number of compounding periods per year
• i effective interest rate per compounding period
• iaeffective interest rate per year

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Calculate Effective Interest Rate

• FP Pia P (1 ia)
• FP(1i)m
• P (1 ia) P(1i)m
• (1 ia) (1i)m
• ia (1i)m - 1 or ia (1r/m)m - 1
• Where r is the nominal annual interest rate

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Example

• What effective interest rate per year is
  equivalent to 16 per year, compounded quarterly?

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Solution

• m4
• i16 /4 4
• ia (1i)m - 1
• (14)4 -1
• 16.99

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Example (4.11, Page 154)

• What nominal interest rate per year is equivalent
  to an effective 16 per year, compounded
  semiannually?

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Solution

• ia 16
• m2
• r?
• 0.16 (1 r/2)2 1
• r 15.41