how much money is invested at 5% compounded continuously for 3 years will yield $820?
820 = x e^(.05*3)
820 = x e^.15
820 = 1.162 x
x = 705.68
$705.78
is there a way to plug that in the calculator cause i got a diff answer.
Well, actually I did plug it in a calculator.
do 820/e^.15
Where do you guys get 1.162x from?
705.78
To find out how much money is invested at 5% compounded continuously for 3 years to yield $820, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the final amount after interest
P = the principal (initial amount invested)
e = Euler's number (approximately 2.71828)
r = annual interest rate (in decimal form)
t = time (in years)
We need to solve for P, so rearranging the formula:
P = A / (e^(rt))
Now, let's substitute the given values into the formula:
A = $820
r = 5% = 0.05 (as a decimal)
t = 3 years
P = $820 / (2.71828^(0.05 * 3))
P ≈ $732.84
Therefore, approximately $732.84 should be invested at 5% compounded continuously for 3 years to yield $820.