Financial Algebra© Cengage Learning/South-Western

Warm-UpWarm-Up

Grab a paper from the back AND pull out Friday’s notes

Manny invests $40,000 in a one year CD paying an annual interest rate of 6.55%. The interest is compounded daily. Find the APY for Manny’s account.

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3-6CONTINUOUS COMPOUNDING

Compute interest on an account that is continuously compounded.

OBJECTIVES

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limit finite infinite continuous compounding exponential base (e) continuous compound interest formula

Key Terms

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How can interest be compounded How can interest be compounded continuously?continuously?

Can interest be compoundedDaily?Hourly?Each minute?Every second?

If $1,000 is deposited into an account and compounded at 100% interest for one year, what would be the account balance at the end of the year?

Financial Algebra© Cengage Learning/South-Western

Continuous CompoundingContinuous Compounding

Interest can also be compounded continuouslyNot just daily, but every second, every micros

second – NON STOPInterest that is continuously compounded

follows the following formula

e = 2.71828

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EXAMPLE 5EXAMPLE 5 If you deposited $1,000 at 100% interest, compounded

continuously, what would your ending balance be after one year?

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EXAMPLE 6EXAMPLE 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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Craig deposits $5,000 at 5.12% interest, compounded continuously for four years. What would his ending balance be to the nearest cent?

CHECK YOUR UNDERSTANDING