Show steps please If you invest $4000 in an account paying 5.6% compounded continuously, how long will it take for your money to accumulate to $7000?

Question

slaaibak · Answer

$$7000 = 4000e^{n * 0.056}$$

$${7000\over4000} = e^{n * 0.056}$$

ln both sides:

$$\ln({7000\over4000}) = \ln(e^{0.056*n})$$

Using ln laws:

mathmate · Answer

If the money is to compound continuously, the formula to use would be:
FV=PVe^(rt)
7000=4000e^(0.056)t
Take log both sides and divide, solve for t to get
t=9.993 years

slaaibak · Answer

$$\ln({7\over4}) = 0.056n * \ln e = 0.056n$$

$$n = { \ln({7\over4}) \over 0.056  }$$

anonymous · Answer

slaaibak. Why does the equation I used give a different value?

slaaibak · Answer

Because if you compound something continuously, the formula is

A = Pe^nr

mathmate · Answer

Your equation is for compound interest.
The question requires a continuous compounding, which means that the compounding period is infinitely short.  It requires the formula involving e.

anonymous · Answer

ty mathmate. Good to know :-)

slaaibak · Answer

To observe why this happens, evaluate the following limit:

$$\ \lim_{x \rightarrow \infty} (1 + {1\over x})^x$$