Sandra invested $2500 at 4% compounded continuously. At the same time, James invested $2650 at 4% compounded monthly. How long will it take for their investments to be equal in value?

Question

Sandra invested $2500 at 4% compounded continuously. At the same time, James invested  $2650 at 4% compounded monthly. How long will it take for their investments to be equal in value?

dumbcow · Answer

$$2500e^{.04t} = 2650(\frac{12.04}{12})^{12t}$$
solve for t using logs

sh3lsh · Answer

Woaah, how'd you set up the equation?

dumbcow · Answer

$$\ln (e^{.04t}) = \ln(\frac{2650}{2500})+\ln(\frac{12.04}{12}^{12t})$$

dumbcow · Answer

from the formulas for compound interest and continuous interest
$$P_{t} = P_{0}(1+\frac{r}{n})^{nt}$$
$$P_{t} = P_{0}e^{rt}$$

dumbcow · Answer

$$.04t = \ln(\frac{2650}{2500}) +12t*\ln(\frac{12.04}{12})$$