Suppose you invest $600 at an annual interest rate of 3.9% compounded continuously. How much will you have in the account after 25 years?
amount=600e^rt
where r= .039 t=25
$1590.70
To calculate how much you will have in the account after 25 years, we can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = the amount of money after time t
P = the principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = the annual interest rate (expressed as a decimal)
t = the time in years
In this case, the principal amount (P) is $600, the annual interest rate (r) is 3.9% (or 0.039 as a decimal), and the time (t) is 25 years.
Now, let's plug in these values into the formula:
A = 600 * e^(0.039 * 25)
To simplify further, we need to calculate e^(0.039 * 25). You can use a scientific calculator or an online calculator to find this value. It turns out to be approximately 2.29257.
Now, let's substitute it back into the formula:
A = 600 * 2.29257
Calculating this, we get:
A ≈ $1375.54
Therefore, after 25 years of continuous compounding at an annual interest rate of 3.9%, you would have approximately $1375.54 in the account.