The formula for continuously compounded interest on a principal investment P at a given interest rate r over time t in years is given by A = Pe^rt. You have deposited $12,000 in an account that pays 4.15% interest, compounded continuously. How long will it take for your initial investment to grow six times its original worth? Round your answer to the nearest tenth.

Question

darkbluechocobo · Answer

@satellite73  could you help me Im not so good with compound interest S:

darkbluechocobo · Answer

would this be 43.2 years?

kropot72 · Answer

$$\large A=Pe^{rt}\ ..............(1)$$
If we divide both sides of (1) by P we get:
$$\large \frac{A}{P}=e^{rt}\ ............(2)$$
In the question it is given that A/P = 6, and r expressed as a decimal is 0.0415. Plugging these values into (2) gives:
$$\large 6=e^{0.0415t}\ ...........(3)$$
Now you just need to solve (3) to find the value of t.

darkbluechocobo · Answer

See this is where it comes difficult for me Because I dont understand how to get an exponent by itself

kropot72 · Answer

Take natural logs of both sides of (3).

darkbluechocobo · Answer

so if natural then would it be 6e?

darkbluechocobo · Answer

im kinda new to log S:

darkbluechocobo · Answer

nvm so ln6=0.0415t?

kropot72 · Answer

Your equation:
$$\large \ln 6=0.0415t$$
is correct. Now you need to divide both sides of the equation by 0.0415 to find the value of t in years.