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Check it outCompound Interest (Continuously)  Problem 1 5,604 views
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!
So when interest is compounded continuously, what it means is that it's compounded the minute it finish calculating your interest it's going to recalculate. We are going to look at a problem.
So for this problem what we have is we invest $3000 at 4% compounded continuously and we're asked how much we have after 4 years?
So we know that it's compounded continuously which tells us we're going to be using our Pert equation a equals Pe to the rt. You invest 3000 which is our initial investment, which is our principal p, that goes the 3000 is the 2 point 7. Rate is our percent that we're dealing with, so that's going to be .04 and our time is 4 as well, so times 4.
So the amount that we are going to have after 4 years is just this expression, you can either leave it as an expression or you can either plug in your calculator, plug in our calculator 3000 e to the .04 times 4 we end up with $3520.53.
So using our Pert equation to figure how much money we have after investing a certain amount we compounded continuously.
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Sample Problems (8)
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Compound Interest (Continuously)
Problem 1 5,603 viewsInvest $3000 at 4% interest compounded continuously.
How much will you have after 4 years? 
Compound Interest (Continuously)
Problem 2 4,727 viewsInvest $5000 at 5% interest compounded continuously.
How long will it take to double? 
Compound Interest (Continuously)
Problem 3 3,977 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? 
Compound Interest (Continuously)
Problem 4 479 views 
Compound Interest (Continuously)
Problem 5 449 views 
Compound Interest (Continuously)
Problem 6 535 views 
Compound Interest (Continuously)
Problem 7 513 views 
Compound Interest (Continuously)
Problem 8 501 views
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