How much money invested at 5% compounded continuously for 3 years will result in $820?
show the steps
The formula to calculate the future value (A) of an investment compounded continuously is given by:
A = P * e^(rt)
Where:
A = Future value
P = Principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = Annual interest rate (as a decimal)
t = Time period in years
In this case, we have the following information:
A = $820
r = 5% = 0.05
t = 3 years
Let's plug in the values and solve for P:
820 = P * e^(0.05 * 3)
Divide both sides of the equation by e^(0.05 * 3):
820 / e^(0.05 * 3) = P
Using a calculator, we can find:
e^(0.05 * 3) ≈ 1.15763
Substituting this value back into the equation:
820 / 1.15763 = P
P ≈ $709.99
Therefore, approximately $709.99 needs to be invested at 5% compounded continuously for 3 years to result in $820.