SOLUTION: - How many months does it take for $1000 to grow to $1500 in an account paying 12% compounded monthly?

Algebra ->  Algebra  -> Exponential-and-logarithmic-functions -> SOLUTION: - How many months does it take for $1000 to grow to $1500 in an account paying 12% compounded monthly?      Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 151295: - How many months does it take for $1000 to grow to $1500 in an account paying 12% compounded monthly?
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
A=P%281%2Br%2Fn%29%5E%28nt%29 Start with the compound interest formula.


1500=1000%281%2B0.12%2F12%29%5E%2812t%29 Plug in A=1500, P=1000, r=0.12 (note: 12%=0.12) and n=12


1500%2F1000=%281%2B0.12%2F12%29%5E%2812t%29 Divide both sides by 1000.


3%2F2=%281%2B0.12%2F12%29%5E%2812t%29 Reduce


3%2F2=%281%2B0.01%29%5E%2812t%29 Divide 0.12%2F12 to get 0.01


3%2F2=%281.01%29%5E%2812t%29 Add 1 to 0.01 to get 1.01


log%2810%2C%283%2F2%29%29=log%2810%2C%28%281.01%29%5E%2812t%29%29%29 Take the log of both sides.


log%2810%2C%283%2F2%29%29=12t%2Alog%2810%2C%281.01%29%29 Rewrite the right side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


log%2810%2C%283%2F2%29%29%2F%2812log%2810%2C%281.01%29%29%29=t Divide both sides by 12log%2810%2C%281.01%29%29.


So the answer is t=log%2810%2C%283%2F2%29%29%2F%2812log%2810%2C%281.01%29%29%29 which approximates to t=3.39574


So it takes about 3.4 years (or 40.8 months) to go from $1,000 to $1,500