Question

So my imaginary buddy mike invested 5000 bucks at 9% interest rate compounded monthly. How many years will it take for my man Mike to double his cash? I got ~8 years. Now for the one i don' t know at all..
So my bro sal invested 5000 dollars at a 5% rate compounded continuously (that's the bit that gets me). How long will it take for -him- to double his cash monies

Answer 1

HI!!

Answer 2

update i got 14 years for prob #2

Answer 3

did you solve
\[e^{.05t}=2\] and get
\[t=\frac{\ln(2)}{.05}\]?

Answer 4

uh..? i did the Pe^rt bit

Answer 5

doubles means set it equal to 2

Answer 6

doesn't matter what you start with

Answer 7

couldn't i solve for 10000 dollars? (which is what i attempted)

Answer 8

because these particular problems had nothing to do with natural logs

Answer 9

the second one does, yes

Answer 10

dang it

Answer 11

5% rate compounded continuously (that's the bit that gets me). How long will it take for -him- to double his cash monies
formula for continuous compounding is \(Pe^{rt}\)
set
\[e^{.05t}=2\] solving needs the log

Answer 12

doesn't e have a set value though? We've got the principle, 5000, e, 2.71812, the rate, .05. we're just missing time, right?

Answer 13

forget the principle, it is unimportant
doubling time is doubling time

Answer 14

\(e\) is a number, but don't mess with the decimal form
solve
\[e^{.05t}=2\] in two steps
1) write in logarithmic form as
\[.05t=\ln(2)\] then
2) divide by \(.05\)

Answer 15

so this begs the question, what is a natural log divided by 2