Section 4.7: Compound Interest. Continuous Compounding Formula P = Principal invested (original amount) A = Amount after t years t = # of years r = Interest.

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Presentation transcript:

Section 4.7: Compound Interest

Continuous Compounding Formula P = Principal invested (original amount) A = Amount after t years t = # of years r = Interest rate

Continuous Compounding Example Justin has an initial investment of $2,500 at 3.85% compounded continuously. a) How much will Justin have in his account after 12 years? b) How long until Justin’s investment reaches $4,000? c) At what rate should Justin have invested his money if he wanted his investment to triple in 20 years?

Continuous Compounding Practice Chloë invests money in a bond trust that pays 7.2% interest compounded continuously. a) If she has $6, after 10 years, determine her initial deposit. b) How long will it take for Chloë’s bond trust to quadruple?

Computing the Effective Rate of Interest Annual Rate Effective Rate Annual Compounding10% Semiannual Compounding10%10.25% Quarterly Compounding10%10.381% Monthly Compounding10%10.471% Daily Compounding10%10.516% Continuous Compounding10%10.517% Effective Rate of Interest: the equivalent annual simple interest rate that would give you the same amount as compounding after 1 year.

Computing the Effective Rate of Interest On January 2, 2004, an investment is placed in an IRA that will pay 8% per annum compounded continuously. a) What is the effective rate of interest?

Section 4.7: Compound Interest Homework #22: Page 322 # 11, 21, 23, 31, 33, 39