MATH AND YOUR MONEY

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MATH AND YOUR MONEY

• A unit on financial management APR and APY

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• Simple interest
• You only earn interest on your original deposit.
  For example, if you deposit 100 in a bank at 5
  yearly simple interest
• Year 1 105
• Year 2 110
• Year 3 115

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• Compound interest
• You earn interest on your interest. For example
  if you deposit 100 in the bank at 5 yearly
  compound interest
• - Year 1 100.05(100)105
• - Year 2 105.05(105)110.25
• - Year 3 110.25 .05(110.25)115.76

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• This all assumes that interest will be paid once
  a year. Sometimes you can have accounts which
  pay interest more than once a year. For example
• Suppose you deposit 100 at 5 annual interest
  and interest is compounded quarterly.
• This means interest is paid once every 3 months.

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How to Compute Quarterly Interest Rate

• Suppose you deposit 1000 at 8 annual percentage
  rate (APR) with quarterly interest
• quarterly interest APR4 84
• 2

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One year of compound investment
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• So at the end of the year your original 1000 is
  1082.43.
• What was the interest rate?
• 8 compounded quarterly
• How much interest did you earn?
• 82.43/1000.082 8.2
• This is called the Annual Percentage Yield (APY)
  of the bank account.

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A Useful Formula

• The compound interest formula for interest paid n
  times per year is
• AP(1 APR/n)(nY)
• where Pstarting principal,
• Ynumber of years (may be a fraction)
• A accumulated balance

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• Lets calculate an example Suppose you invest
  5000 for five years in an account that pays an
  APR of 6 and compounds interest monthly
• AP (1 APR/n)(nY)
• 5000 (1.06/12)(125)
• 5000 (1.005)60
• 6744.25

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• You can calculate the APY for this account by
  simply figuring out what would happen at the end
  of one year
• A P (1APR/12)(121)
• 5000(1.06/12)12
• 5000(1.005)12
• 5308.39

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• So you earned 308.39 interest on this account at
  the end of the year which is
• 308.39/5000, approximately 6.2 APY

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• You can compound daily (but be careful, most
  banks will divide the APR by 360 rather than 365
  to compute the interest rate), or even
  continuously. The formula for continuous
  compounding involves the exponential function,
  which we will visit later.