WARM UP If you deposit $10,000 into an account

earning 3.5% interest compounded quarterly;How much will you have in the account

after 15 years?How much more money will you have after

15 years if you compound the money daily?

COMPOUNDING INTEREST ACTIVITY With a partner, complete the following.

Given $1 invested at 100% for 1 year, find the following compounds. Round all answers to the ten-thousandths. Annually? Quarterly? Monthly? Weekly? Daily? Hourly? Every minute? Every second?

What do you notice about the answers as you compound more frequently?

What special number is it?

CONTINUOUSLY COMPOUNDING Growth and Decay

Examples from science/nature.http://

www.dnatube.com/video/12203/Rapid-Bacterial-Growth

Example: If a bacteria doubles every 20 minutes, What is its constant or rate of growth? If it continues to grow at that rate how much

bacteria will be present in 4 hours?

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PRACTICE If your account compounds quarterly at

6.75%;How much will you have to invest to have

$8,000 in 15 years.How much if you compound continuously?

If a radio-active material has a half life of 65 years;How much will be present in 10 years?How long until a 100 mg sample decays to 5

mgs?

SUMMARY How do you tell which compounding

formula to use? What types of things compound

continuously? If you deposited $10,000 in an account

earning 2.75% compounded quarterly;How much money will you have in 15 years?How much more would you have if it was

compounded continuously? If the half-life of a toxic chemical is 75

years, how long until a 500mg sample has reduced to 35 mg?