If $ 2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $ 7500 at 8%?
2500 e^(.08t) = 7500
e^(.08t) = 3
take ln of both sides and solve for t
To find out how long it will take for $2500 to grow to$7500 at 8% interest compounded continuously, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A is the final amount ($7500 in this case)
P is the initial amount ($2500 in this case)
e is Euler's number (approximately 2.71828)
r is the interest rate (8% or 0.08 in decimal form)
t is the time in years (what we're trying to find)
By rearranging the formula, we can solve for t:
t = ln(A/P) / r
Now, let's substitute the known values into the formula and calculate the time required:
t = ln(7500/2500) / 0.08
First, we divide 7500 by 2500:
t = ln(3) / 0.08
Next, we take the natural logarithm (ln) of 3:
t ≈ 1.0986 / 0.08
Finally, we divide 1.0986 by 0.08:
t ≈ 13.7325 years
Therefore, it will take approximately 13.73 years for the initial investment of $2500 to grow to $7500 at a continuous interest rate of 8%.