How much money invested at 5% compounded continuously for 3 years will result in $820?
The formula for compound interest when interest is compounded continuously is given by:
A = P * e^(rt)
Where:
A = final amount
P = principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = interest rate
t = time (in years)
We are given the following information:
A = $820
r = 5% = 0.05
t = 3 years
Let's solve for P:
820 = P * e^(0.05 * 3)
To find P, divide both sides by e^(0.15):
820 / e^(0.15) ≈ P
Calculating this value gives:
P ≈ 820 / 1.161833 ≈ $705.68
Therefore, an investment of approximately $705.68 at a 5% interest rate compounded continuously for 3 years will result in $820.