It would take approximately 4.87 years for $600 to amount to $930 at 9% compounded continuously.
Sure, here is the explanation of how long it would take for $600 to amount to $930 at 9% compounded continuously.
Formula-
The formula for continuously compounded interest is:
A = P * e^(rt)
where:
A is the ending amount
P is the principal amount (initial investment)
e is the base of the natural logarithm (approximately 2.71828)
r is the annual interest rate
t is the time in years
Calculation
In this case, we are trying to find the value of t for the following:
P = $600
A = $930
r = 9% = 0.09
We can rearrange the formula to solve for t:
t = ln(A / P) / r
Plugging in the values, we get:
t = ln(930 / 600) / 0.09
t ≈ 4.87 years
Therefore, it would take approximately 4.87 years for $600 to amount to $930 at 9% compounded continuously.