Question 1054609

How would you solve the questions:

How long will it take for $1400 dollars to grow to $11,900 at an interest rate of 2.3% if the interested is compounded quarterly?  I am taking the amount and dividing it by the initial investment. My next step has been to plug the following into my TI 84 calculator:

log(1+.023)8.5

Can you tell me what I am doing wrong? I get 8.6 years but the correct answer should be 20.65 years. 

Thank you
<pre>It CANNOT be 20.65 years. That's IMPOSSIBLE! It's just too short a time!
You must be either looking at the wrong answer or failed to include the correct figures.
{{{A = P(1 + i/m)^(mt)}}}
{{{"$11,900" = "$1,400"(1 + .023/4)^(4t)}}} ------ Substituting $11,900 for A, $1,400 for P, .023 for i, and 4 (quarterly) for m
{{{"$11,900"/"$1,400" = 1.00575^(4t)}}} ------ Dividing both sides by $1,400, and simplifying {{{1 + .023/4}}}
{{{8.5 = 1.00575^(4t)}}}
{{{4t = log (1.00575, 8.5)}}} ------- Converting to LOGARITHMIC form
{{{4t = log (8.5)/log (1.00575)}}} ------ Applying change of base
{{{highlight_green(matrix(1,16, t, or, time, "=", (log (8.5)/log (1.00575))/4, or, log (8.5)/log (1.00575), "÷", 4/1, or, log (8.5)/log (1.00575), "*", 1/4,  "=", 93.31361, years))}}}