Show all your the steps. Use the continuously compounded Interest: A(t)=p*e^rt
How much money invested at 6% compounded continuously for 5 years will result in $916?
To find the amount of money invested at 6% compounded continuously for 5 years that will result in $916, we can use the formula for continuously compounded interest:
A(t) = P * e^(rt)
Where:
A(t) = the amount of money after t years ($916 in this case)
P = the principal amount (the money initially invested)
r = the annual interest rate (6% or 0.06)
t = the number of years (5 years)
Given that A(t) = $916, r = 0.06, and t = 5, we can plug these values into the formula and solve for P:
$916 = P * e^(0.06*5)
Divide both sides by e^(0.3) to isolate P:
P = $916 / e^(0.3)
P ≈ $682.15
Therefore, approximately $682.15 invested at 6% compounded continuously for 5 years will result in $916.