How long does it take to double an investment of $5000 at 9% per year if the account compounds continuously?
To determine how long it takes to double an investment at a given interest rate with continuous compounding, you can use the continuous compound interest formula:
A = P * e^(rt)
Where:
A = final amount
P = principal amount (initial investment)
e = Euler's number (approximately 2.71828)
r = interest rate (as a decimal)
t = time (in years)
In this case:
P = $5000
r = 9% = 0.09 (as a decimal)
A = 2 * P = 2 * $5000 = $10000
Now, we can rearrange the formula to solve for t:
t = ln(A / P) / r
Here, ln represents the natural logarithm.
Substituting the known values:
t = ln($10000 / $5000) / 0.09
Calculating this equation will give you the time it takes to double the investment with continuous compounding.
e^(.09t) = 2
now solve for t years