Question

How long would it take $3500 to grow to $8400 if the annual rate is 4.9% and interest is compounded monthly?

Answer 1

\[8400=3500(1+\frac{.049}{12})^{12t}\] solve for t

Answer 2

any idea how to do this?
you need logs

Answer 3

when it comes to logs i am beyond lost ! to simplify i am going to do whats in the () first

Answer 4

ok the first thing you need handy is a calculator

Answer 5

and the next thing before messing around in the parentheses is to divide both sides by 3500

Answer 6

2.4

Answer 7

i.e. start with
\[2.4=(1+\frac{.049}{12})^{12t}\]

Answer 8

right

Answer 9

now with careful use of a calculator we can solve for \(12t\) in one step

Answer 10

the idea is this
to solve
\[b^x=A\] you get
\[x=\frac{\ln(A)}{\ln(b)}\]

Answer 11

in this example \(A=2.4,b=(1+\frac{.049}{12})\)

Answer 12

so you get
\[12t=\frac{\ln(2.4)}{\ln(1+\frac{.049}{12})}\]

Answer 13

of course we want \(t\) not \(12t\) so your actual answer is
\[t=\frac{\ln(2.4)}{12\ln(1+\frac{.049}{12})}\]

Answer 14

i get 17.9 carefully using parenthese and a calculator (ok wolfram)
http://www.wolframalpha.com/input/?i=ln%282.4%29%2F%2812%28ln%281%2B.049%2F12%29%29%29

Answer 15

to recap, the idea is to get it to look like
\[b^x=A\]so you can write
\[x=\frac{\ln(A)}{\ln(b)}\] the log of the total divided by the log of the base

Answer 16

when you were putting the equation in to wolframaalpha.com why is there the 3 () at the end ?

Answer 17

because ... let me go back and look

Answer 18

ok i didn't really need it. here it is with few parentheses
http://www.wolframalpha.com/input/?i=ln%282.4%29%2F%2812ln%281%2B.049%2F12%29%29

Answer 19

thank you so much

Answer 20

just be careful to put parenthese around the whole denominator
and if you are using wolfram you can tell if it looks right because it shows you what it is computing
yw

Answer 21

yes that site is gonna be a huge help to me !