how long will it take $1250 to become $2000 at 3.5% interest compounded continuously? (round to nearest tenth of a year)
To calculate the time it takes for an amount to grow using continuous compounding, we can use the formula:
A = P*e^(rt),
where:
A is the final amount,
P is the initial principal,
e is Euler's number (approximately 2.71828),
r is the interest rate, and
t is the time in years.
In this case, we want to find the time (t), given the initial principal (P = $1250), the final amount (A = $2000), and the interest rate (r = 3.5% or 0.035).
Rearranging the formula to solve for t, we have:
t = ln(A/P) / r.
Now, let's plug in the given values:
t = ln($2000/$1250) / 0.035.
Using a calculator to evaluate the expression, we find:
t ≈ ln(1.6) / 0.035 ≈ 1.221 / 0.035 ≈ 34.89 years.
Therefore, it will take approximately 34.9 years for $1250 to become $2000 with a continuous interest of 3.5%.