Compound Interest

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Compound Interest

• Ross Chapman
• Brandon Miller

Finance 321 Stephen DArcy 830 AM
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• Simple Interest You only receive interest on
  your initial investment, meaning every period you
  take the interest out of your account and the
  interest grows on the initial investment.
• Investment x (1 t i) value after t- years
• This is not a very efficient way to invest your
  money.

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Simple Interest Example

• Suppose you invest 10,000 in a bank, which pays
  you simple interest of 12 annually. How much
  will you have in your bank account after five
  years?

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Simple Interest Solution

• 10,000 (1 5 .12) 16,000

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• Compound Interest each interest payment is
  reinvested to earn more interest in subsequent
  periods.
• Investment (1 i) t Value at time t

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Compound Interest Example

• Suppose you put 10,000 into a CD at your local
  bank, at a rate of 12 compounded annually for 5
  years. How much will you have when you take out
  the principle and interest at the end of the 5
  years.

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Annual interest solution

• 10,000(1.12)5 17,623.42

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More Compound Interest
Sometimes the interest wont be compounded
annually, but rather m times a year.

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More Compound Interest

• If the interest is convertible mth-ly then
• The interest rate your money is compounded at
  is i/m
• Investment x (1i/m)tm Value at time t

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More Compound Interest

• If you want to know the equivalent annually
  compounded rate to the interest rate compounded
  mth-ly
• Then use this formula
• ia ((1 i/m)m) - 1

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Compound Interest Example

• Say you put 10,000 into the bank at 12
  convertible monthly for 5 years. How much do you
  have in your account after 5 year? What is the
  equivalent annual compounded rate?

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Compound Interest Answer

• First Question
• 10000 x (1 .12/12) 5 12 18,166.97
• Second Question
• ia ((1 .12/12) 12) 1 12.68

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Continuously Compounded Interest

• If you money is compounded continuously that
  means at all times its earning interest.
• Principal ert (Pert)
• Equivalent Annual Compounded Rate
• (Accumulate Value/ Investment)(1/t) - 1

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Continuously Compounded Interest

• Say you 10000 in the bank at 12 compounded
  continuously. How much money do you have after 5
  year? What is the equivalent annual compounded
  rate?

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Answer

• Accumulated Value
• 10000 e(.12)5 18,221.19
• Equivalent Annual Compounded Rate
• (18221.19/10000)(1/5) -1 12.75

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• So as you can see as m increases in size the
  amount of interest you earn in the year grows.

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The End!

• Any Question?