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Money, Interest Rates and Growth Functions

APR or Nominal Interest Rate compared to Effective Interest Rate

  1. You invest an amount of money at 5%, (a) compounded yearly, (b) compounded monthly, (c) compounded daily and (d) compounded continuously. What are the nominal and effective rates for each investment?
    • 5% compounded yearly
    • APR = Nominal rate = 5%
    • Return = (1+ .05/1)1 = 1.05, effective rate is 0.05 or 5% (same as nominal)

    • 5% compounded monthly
    • APR = Nominal rate= 5%
    • Return = (1 + .05/12)12 = 1.05116, effective rate is 0.0512 (rounded) or 5.12%

    • 5% compounded daily
    • APR = Nominal rate = 5%
    • Return = (1 + .05/365)365 = 1.05127, effective rate is 0.0513 (rounded)or 5.13%

    • 5% compounded continuously
    • APR = Nominal rate = 5%
    • Return = e.05 = 1.05127, effective rate is 0.0513 (rounded ) or 5.13%
  2. You invest $1,000 and 8 years later you have $1,900. What is the interest rate if interest was compounded monthly?
    1. 1,900 = 1000 ( 1 + r/12 )(12*8)
    2. 1,900/1000 = (1 + r/12)(12*8)
    3. (1.9)1/96 = [(1 + r/12) ]1/96
    4. 1.0006708 = ( 1 + r/12 )
    5. r/12 = 1.006708 - 1
    6. r = 12(0.006708) = 0.0805, The interest rate was 8.05% (rounded)