3­6 Continuous Compounding Short Version.notebook
November 07, 2014
Bellwork 11-7-14
The infinite! No other question has ever moved so profoundly the spirit of men.
David Hilbert, Mathematician
1. Can interest be compounded: daily, hourly, every minute,
every second?
2. If $1,000 is deposited into an account and compounded
continuously at 100% interest for one year, what would be the
account balance at the end of the year?
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3­6 Continuous Compounding Short Version.notebook
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November 07, 2014
CONTINUOUS COMPOUNDING
OBJECTIVES
Compute interest on an account that is continuously compounded. 2
3­6 Continuous Compounding Short Version.notebook
November 07, 2014
Key Terms
• limit
- a concept in calculus which
means an unreachable value
• finite
- something that has an end
and can be represented by
a real number
• infinite
- something without end,
that cannot be represented
by a real number
• continuous compounding
- a method of calculating interest
so that it is compounded an infinite
number of times
• exponential base (e)
- an irrational number, with an
approximate value of e=2.718
• continuous compound interest formula
- a formula for calculating
continuous compound interest
B= pert
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3­6 Continuous Compounding Short Version.notebook
November 07, 2014
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3­6 Continuous Compounding Short Version.notebook
November 07, 2014
EXAMPLE 5
If you deposited $1,000 at 100% interest, compounded continuously, what would your ending balance be after one year? 5
3­6 Continuous Compounding Short Version.notebook
November 07, 2014
EXAMPLE 6
If you deposit $1,000 at 4.3% interest, compounded continuously, what would your ending balance be to the nearest cent after five years?
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3­6 Continuous Compounding Short Version.notebook
November 07, 2014
CHECK YOUR UNDERSTANDING
Craig deposits $5,000 at 5.12% interest, compounded continuously for four years. What would his ending balance be to the nearest cent? 7
3­6 Continuous Compounding Short Version.notebook
November 07, 2014
Homework: Page 154-155 #s 1-6
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