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How much money invested at 6% compounded continuously for 5 years will result in $916?
To solve this problem, we need to use the formula for compound interest compounded continuously:
A = P*e^(rt)
Where:
A = final amount after 5 years ($916)
P = initial principal (the amount of money invested)
r = annual interest rate (6% or 0.06)
t = time in years (5 years)
e = Euler's number, approximately 2.71828
We want to solve for P. So, the formula becomes:
916 = P*e^(0.06*5)
First, calculate e^(0.06*5):
e^(0.06*5) = e^(0.3) ≈ 1.349
Now substitute this back into the equation:
916 = P*1.349
Now, isolate P by dividing both sides by 1.349:
P = 916 / 1.349
P ≈ $678.29
So, the amount of money that needs to be invested at 6% compounded continuously for 5 years to result in $916 is approximately $678.29.