Question

how long will it take $10,000 invested at 5% compounded continuously to grow to $25,000?

Answer 1

(10000) * (1.05^x) = 25000.
Solve for x.

Answer 2

thank you

Answer 3

from where you got 1.05?? the percentage is 0.05^x

Answer 4

Continuous Compound Formula:

\[A = Per^t\]

A=Account Balance = 25,000
P=Principal = 10,000
r=rate (decimal form) = 0.05
t=time (in years) = what you need to find

\[25,000 = 10,000e^{(0.05)t}\]

Answer 5

In order to solve this, you will eventually, have to take logs. For now, start by dividing both sides by 10,000

Answer 6

\[\frac{25000}{10000} = e^{(0.05)t}\]\[2.5 = e^{(0.05)t}\]

Answer 7

Next, take logs of both sides:

\[\log(2.5) = \log(e^{(0.05t)})\]
\[log(2.5) = t\log(e^{0.05})\]

Answer 8

i divided 25,000/10,000 = 10,000e(0.05)t/10,000 =
2.5=1.0512t both side divided by 1.0512 t=2.4

Answer 9

\[\frac{\log(2.5)}{\log(1.051271)} = t\]

Answer 10

ok

Answer 11

We're using logs..so please remember that

Answer 12

i punch it in the calculator and i got 18.33 for t

Answer 13

Good job

Answer 14

thanks to you

Answer 15

If you use my formula, you get the most precise result.

Answer 16

If you use virgil's formula, you still get 18, but you get the wrong approximation of months.

Answer 17

yeah but i am really dumb when it come to logs and logarithm

Answer 18

Well, there are some things you can do to make your life easier. My rule is to "only take logs when you need to".

Answer 19

i will follow that too thank you