### 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)