Answer:
Explanation:
The formula for continuously compounded interest is:
A = Pe^(rt)
where:
A = the final amount
P = the initial amount
r = the annual interest rate (as a decimal)
t = the time (in years)
We can use this formula to solve for t, the time it takes for $50 to grow to $130 at a 7% annual interest rate compounded continuously.
First, let's plug in the given values:
$130 = $50e^(0.07t)
Next, let's solve for t by isolating it on one side of the equation:
e^(0.07t) = $130/$50
e^(0.07t) = 2.6
Take the natural logarithm of both sides:
ln(e^(0.07t)) = ln(2.6)
0.07t = ln(2.6)
Solve for t:
t = ln(2.6)/0.07 ≈ 13.4 years
Therefore, it takes approximately 13.4 years for $50 to grow to $130 at a 7% annual interest rate compounded continuously.