How much money invested at 5% compounded continuously for 3 years will result in $820? show all steps
The formula for compound interest is given by:
A = P * e^(rt)
Where:
A = the amount of money accumulated after n years, including interest
P = the principal amount (initial investment)
r = annual interest rate (decimal)
t = time the money is invested for
e = Euler's number, approximately equal to 2.71828
Given that A = $820, r = 0.05, and t = 3, we need to solve for P:
820 = P * e^(0.05*3)
820 = P * e^(0.15)
820 = P * 1.16177
P = 820 / 1.16177
P ≈ $705.69
Therefore, to have $820 after 3 years with a continuous interest rate of 5%, you should invest approximately $705.69.