Question

Find the t required for a $1200 investment to double at interest rate r, compound continuously.

Answer 1

what was wrong with the same question you posted in the general math section?

Answer 2

tmi
doubling time has nothing to do with the initial investment
i invest $50 and @amistre64 invests $700,000
mine double to $100 and his doubles to $1,400,000 in the same amount of time

it rains on the just and the unjust

Answer 3

indeed.

and we will need to recall the formula for continuous compounding interest rates

Answer 4

just unsure how to solve for t

Answer 5

you need to know the formula for continuous compounded interest. Then solving for t will be rather simple

Answer 6

A=Pe^rt from what I know, but not that simple to me really...

Answer 7

lets redefine A, we want it to be 2P right?

Answer 8

yes

Answer 9

... fixing a few typos

A=Pe^rt

now lets start peeling away the layers to get to "t"

2P = Pe^rt ; divide each side by P

2 = e^rt ; ln undoes an e

ln(2) = rt

now it just a matter of removing the r ....

Answer 10

well r is given as 0.062

Answer 11

I'm sorry for not stating so from the start, slipped my mind

Answer 12

can you solve: ln(2) = rt , for t?

Answer 13

divide both sides by r?

Answer 14

correct soo

ln(2)/r = t

use a calculator and plug in the value for r to determine t

Answer 15

11.17

Answer 16

and note that when @amistre64 writes
2P = Pe^rt ; divide each side by P
2 = e^rt ;

it means that the initial amount is a red herring.
doubling time is doubling time

Answer 17

oh I see. Thank you so much