# Thread: continous interest

1. ## continous interest

The rate of a continuous money flow starts at $1000 and decreases exponentially at 4% per year for 10 years. Find the final amount if interest is earned at 6% compounded continuously. 2. Originally Posted by harry The rate of a continuous money flow starts at$1000 and decreases exponentially at 4% per year for 10 years. Find the final amount if interest is earned at 6% compounded continuously.
You will not get much help with this as it is so obscurely worded that
I suspect most of the helper don't understand what is being asked here.

RonL

3. Originally Posted by harry
The rate of a continuous money flow starts at $1000 and decreases exponentially at 4% per year for 10 years. Find the final amount if interest is earned at 6% compounded continuously. CaptainBlack is right. I read this over and over to see if I was misreading the question. Anyway, I’ve decided to take a stab at it. So we start with$1000 and this money is decreasing exponentially. But then, it is gaining interest while it is decreasing. So the principle at any time is given by A(t) where:

A(t) = 1000*e^-0.04t
Now we will use this as the initial amount in the formula for continuous compounding at 6%, that is, use it as P0 in:

P(t) = P0*e^0.06t

=>P(t) = (1000*e^-0.04t)*e^0.06t
……...= 1000*e^0.02t

=> P(10) = 1000*e^0.02(10)
………...= 1000*e^0.2
……….~= 1221.40

Does this make sense guys?

### the rate of a continuous money flow starts at

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