Section 10.2 Compound Interest

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Section 10.2 Compound Interest

• Simple interest is generally used for loans of
  one year or less. For loans of more than one
  year, the interest paid on the money borrowed
  usually use compound interest.
• Compound interest is interest calculated not only
  on the original principal, but also on any
  interest that has already been earned.

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Compound Interest Formula

• The compound amount formula is
• A P (1 i)N
• where A is the compound amount when P dollars are
  deposited at an interest rate of i per
  compounding period for N compounding periods.
  Because i is the interest rate per compounding
  period and n is the number of compounding periods
  per year,
• i r / n N n t

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Example

• How much interest is earned in 6 years on 8000
  deposited in an account paying 9 interest,
  compounded monthly?

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Example

• Determine the compound amount when 2000 is
  deposited in an account earning an interest rate
  of 12, compounded quarterly, for 10 years.
• CHECK YOUR PROGRESS
• Determine the compound amount when 3500 is
  deposited in an account earning an annual
  interest rate of 6, compounded semiannually, for
  5 years.

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Present Value Formula

• The present value formula is
• where P is the original principal invested at an
  interest rate of i per compounding period for N
  compounding periods, and A is the compound amount.

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EXAMPLE

• How much money should be invested in an account
  that earns 8 interest, compounded quarterly, in
  order to have 30,000 in 5 years?

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Check your progress

• How much money should be invested in an account
  that earns 9 interest, compounded semiannually,
  in order to have 20000 in 5 years?

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Inflation

• Inflation is an economic condition during which
  there are increases in the costs of goods and
  services.
• EXAMPLE
• Suppose your annual salary today is 35,000. You
  want to know what an equivalent salary will be in
  20 years that is, a salary that will have the
  same purchasing power, if the annual inflation
  rate is 4.

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Effective Interest Rate

• When interest is compounded, the annual rate of
  interest is called the nominal rate. The
  effective rate is the simple interest rate that
  would yield the same amount of interest after one
  year. When a bank advertises a "7 annual
  interest rate compounded daily and yielding
  7.25, the nominal interest rate is 7 and the
  effective rate is 7.25.

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Formula (1i)N - 1

• Example 10. Calculate the Effective Interest Rate
• A credit union offers a certificate of deposit at
  an annual interest rate of 8, compounded
  monthly. Find the effective rate. Round to the
  nearest hundredth of a percent.

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EXAMPLE 11. Compare Annual Yields

• One bank advertised an interest rate of 6
  compounded quarterly, on a certificate of
  deposit. Another bank advertises an interest rate
  of 5.85 compounded monthly. Which investment has
  the higher annual yield?