SOLUTION: Find the number of years it will take for $17,000 to grow to $18,221.60 at 7% interest compounded quarterly.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Find the number of years it will take for $17,000 to grow to $18,221.60 at 7% interest compounded quarterly.      Log On


   

Question 1103291: Find the number of years it will take for $17,000 to grow to $18,221.60 at 7% interest compounded
quarterly.
Answer by Edwin McCravy(20065) About Me  (Show Source):
You can put this solution on YOUR website!
A=P%281%2Br%2Fn%29%5E%28nt%29

We solve for t before substituting, because it's
easier than substituting first:

ln%28A%29=ln%28P%281%2Br%2Fn%29%5E%28nt%29%29

ln%28A%29=ln%28P%29%2Bln%281%2Br%2Fn%29%5E%28nt%29

ln%28A%29=ln%28P%29%2B%28nt%29ln%281%2Br%2Fn%29

Divide both sides by %28n%29ln%281%2Br%2Fn%29

%28ln%28A%29-ln%28P%29%29%2F%28%28n%29ln%281%2Br%2Fn%29%29=t

A = final amount = $18221.60
P = beginning amount =$17000
n = number of compoundings per year = 4 (since it's quarterly)
r = 7% as a decimal, 0.07
t = number of years = ???

Plug in:

t=%28ln%2818221.60%29-ln%2817000%29%29%2F%28%284%29ln%281%2B0.07%2F4%29%29

t=%220.9999972068...%22

Rounds to 1 year.

Edwin