Question 183182
You deposit $800 in an account that pays 9% annual
interest compounded monthly. About how many years 
will it take for the account balance to reach $2400? 
Convert this to years and months.
<pre><font size = 4 color = "indigo"><b>
{{{A = P(1+R/N)^(NT)}}}

where A = Final Amount = $2400
      P = Beginning Amount = $800
      R = Rate expessed as a decimal = .09
      N = Number of compoundings per year = 12
      T = Number of years = ?  (What we must find)

We substitute for all but T

{{{A = P(1+R/N)^(NT)}}}
{{{2400 = 800(1+.09/12)^(12T)}}}
{{{2400 = 800(1.0075)^(12T)}}}
{{{2400/800 = (800(1.0075)^(12T))/800}}}
{{{3 = (1.0075)^(12T)}}}
{{{ln(3)=ln(1.0075)^(12T)}}}
{{{ln(3)=12T*ln(1.0075)}}}
{{{ln(3)/(12ln(1.0075))=T}}}
{{{ln(3)/(12ln(1.0075))=T}}} 
{{{1.098612289/(12*.0074720148)=T}}}

{{{12.25252171=T}}}

12 years

To get the months, multiply the decimal 
part {{{.25252171}}} by 12

{{{3.030260563}}} months

or about 12 years, 3 months.

Edwin</pre>