###### Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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# Compound Interest (Continuously) - Problem 1

Carl Horowitz
###### Carl Horowitz

University of Michigan
Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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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.