How much money invested at 6% compounded continuously for 5 years will result in $916?
The formula for compound interest is given by the equation:
A = P * e^(rt)
Where:
A = the amount of money accumulated after n years, including interest.
P = the principal amount (the initial amount of money invested).
r = annual interest rate (decimal).
t = number of years the money is invested for.
e = Euler's number, approximately equal to 2.71828.
Given that A = $916, r = 6% or 0.06, and t = 5 years, we need to find P.
916 = P * e^(0.06*5)
916 = P * e^(0.3)
916 = P * 1.349858807
P = $916 / 1.349858807
P ≈ $678.88
Therefore, approximately $678.88 must be invested at 6% compounded continuously for 5 years in order to accumulate $916.