4'7 Compound Interest

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4.7 Compound Interest
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Principal

• The total amount borrowed.

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Rate of Interest

• The amount charged for the use of the principal.

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Simple Interest Formula

• I P r t
• I the interest charged.
• P the principal borrowed.
• r interest rate (decimal)
• t time in years

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Simple Interest Formula

• Use to calculate the interest on the principal
  given a rate and a time period in years.

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Compound Interest Formula

• Use when the investment is compounded in a
  typical payment period. See next slide.

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Typical Payment Periods

• AnnuallyOnce per Year
• SemiannuallyTwice per Year
• QuarterlyFour times per year
• Monthly12 times per year
• Daily365 times per year

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Compound Interest Formula

• A P(1(r/n))nt
• A amount in the account
• P principal borrowed
• r annual interest rate(decimal)
• n times per year compounded

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Future Value

• A

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Present Value

• P

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Compounded Continuously

• A P ert
• A amount in account after t years.
• r interest rate(decimal)
• t time in years

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Compounded Continuously

• Use this formula when the investment is
  compounded continuously.

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Compounding Interest Examples

• 4,10,

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Present Value Formulas

• Use these when you know how much money you want
  to make and want to know how much you need to
  invest. Remember that the formula with e is used
  when the investment is compounded continuously.

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Present Value Formulas

• Compounded yearly,monthly,etc.
• P A (1 (r/n))-rt
• Compounded Continuously
• P A e-rt

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Present Value Examples

• 16,20,34,36,38