Find the accumulated value of an investment of $3000 at 9% compounded continuously for 3 years.
Isn't the formula 3000e(0.09)x(3)??..which would be $2,201.81...but its wrong?!!..any suggestions would be greatly appreciated
Try
3000e^(.09 x 3)
To find the accumulated value of an investment compounded continuously, we can use the following formula:
A = P * e^(r * t)
where:
A = accumulated value
P = initial investment
r = interest rate
t = time in years
e = Euler's number (approximately 2.71828)
In this case, we have:
P = $3000
r = 9% = 0.09
t = 3 years
Substituting these values into the formula, we get:
A = 3000 * e^(0.09 * 3)
Using a calculator or a programming language that supports exponential functions, we can evaluate this expression.
Using the suggested formula, we have:
A = 3000 * e^(0.09 * 3)
A ≈ 3000 * 2.46630346238
A ≈ $7398.91 (rounded to the nearest cent)
So, the accumulated value of the investment after 3 years at a continuous compounding rate of 9% is approximately $7398.91.