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. Slide 1

Financial Algebra © Cengage/South-Western Slide CONTINUOUS COMPOUNDING Compute interest on an account that is continuously compounded. OBJECTIVES

Financial Algebra © Cengage Learning/South-Western Slide 3 limit finite infinite continuous compounding exponential base ( e ) continuous compound interest formula Key Terms

Financial Algebra © Cengage Learning/South-Western Slide 4 How can interest be compounded continuously? Can interest be compounded Daily? 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 Compounding Interest can also be compounded continuously Not just daily, but every second, every micros second – NON STOP Interest that is continuously compounded follows the following formula e = Slide 5

Financial Algebra © Cengage Learning/South-Western Slide 6 EXAMPLE 5 If you deposited $1,000 at 100% interest, compounded continuously, what would your ending balance be after one year?

Financial Algebra © Cengage Learning/South-Western Slide 7 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?

Financial Algebra © Cengage Learning/South-Western Slide 8 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