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Compound Interest (Continuously)  Concept
Carl Horowitz
Carl Horowitz
University of Michigan
Runs his own tutoring company
Carl taught upperlevel math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!
Problems that involve continuous compound interest use a different equation from problems that have finitely compounded interest, but the continuous compound interest equation is also an exponential equation. We use many of the same methods for calculating continuous compound interest as we do finitely compounded interest. To calculuate compound interest, we can use logarithms and methods for solving exponential equations.
Compounding interest continuously, so sometimes when we compound interest what we do so is actually compound it continuously which means the minute the second you compound an interest you then recalculate it, so we could either compound a set number of times so either every month, day, week whatever it is or continuously which basically is boom boom boom so on and so forth every split second you're recalculating and when we're using continuously we have a different formula okay? It's what I call the part formula a equals pe to the rt okay, a is your ending amount p is your principal or the amount you started with, e is the same e as natural log so the 2.7 so on and so forth, r is your rate which is going to be expressed as a decimal so if you have 5% it'll be 0.05 and time is the amount of time you have your investment in years.
So part equals pe of rt we use this on whenever we're calculating interest that has been compounded continuously.
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Carl Horowitz
B.S. in Mathematics University of Michigan
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Concept (1)
Sample Problems (8)
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Compound Interest (Continuously)
Problem 1 7,384 viewsInvest $3000 at 4% interest compounded continuously.
How much will you have after 4 years? 
Compound Interest (Continuously)
Problem 2 6,670 viewsInvest $5000 at 5% interest compounded continuously.
How long will it take to double? 
Compound Interest (Continuously)
Problem 3 5,524 viewsYou invest $2000 at 5% interest compounded monthly. After two years you switch your money to an account that gives 6% compounded continuously.
How much money do you have 10 years after your initial investment? 
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