How long will it take an investment to triple in value if the interest rate is 4% compounded continuously?
i know its set up as 3x=x(e^rt)
but im confused as what to do nxt
You asked this question twice. Refer to your other post.
To find out how long it will take for an investment to triple in value with a 4% interest rate compounded continuously, you can use the formula for continuous compound interest:
A = P * e^(rt)
Where:
A = final amount (in this case, triple the initial value)
P = principal (initial value of the investment)
r = interest rate (as a decimal)
t = time in years
e = Euler's number, approximately 2.71828
Since you want the investment to triple, you'll set A = 3P:
3P = P * e^(0.04t)
Divide both sides of the equation by P:
3 = e^(0.04t)
To solve for time (t), you'll need to take the natural logarithm (ln) of both sides of the equation:
ln(3) = 0.04t
Divide both sides of the equation by 0.04:
t = ln(3) / 0.04
Now you can use a calculator or a math tool to calculate the value of ln(3)/0.04, which will give you the number of years it will take for the investment to triple in value with a 4% interest rate compounded continuously.