Question 154536
How long would it take for $100 to become $1000 if it is invested at an 8% annual interest rate that is compounded quarterly?
<pre><font size = 4 color = "indigo"><b>

{{{A = P(1+r/n)^(nt)}}}

where P = beginning amount = 100
      A = final amount = 1000 
      r = rate expressed as a decimal = .08
      n = 4 (quarterly means compounded 4 times a year)
      t = ? (number of years, the unknown)

{{{1000 = 100(1+.08/4)^(4t)}}}

{{{1000 = 100(1+.02)^(4t)}}}

{{{1000 = 100(1.02)^(4t)}}}

Divide both sides by 100

{{{10 = (1.02)^(4t)}}}

Take logs of both sides:

{{{log(10) = log(1.02^(4t))}}}  

Use the rule of logs:  {{{log(A^C)=C*log(A)}}}

{{{log(10) = 4t*log(1.02)}}}

Divide both sides by (4*log(1.02))

{{{log(10)/(4log(1.02)) = t}}}

29.06918686 years.

Edwin</pre>