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.
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
=> P(10) = 1000*e^0.02(10)
Does this make sense guys?