SOLUTION: How long will it take for $7 000 to double if it is invested at 6.0% annual interest compounded 9 times a year?

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Question 190666: How long will it take for $7 000 to double if it is invested at 6.0% annual interest compounded 9 times a year?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
A=P%281%2Br%2Fn%29%5E%28nt%29 Start with the compounding interest formula


14000=7000%281%2B0.06%2F9%29%5E%289t%29 Plug in A=14000 (this is double of 7000), P=7000, r=0.06 and n=9


2=%281%2B0.06%2F9%29%5E%289t%29 Divide both sides by 7000.


2=%281%2B0.00667%29%5E%289t%29 Divide


2=%281.00667%29%5E%289t%29 Combine like terms.


log%2810%2C%282%29%29=log%2810%2C%28%281.00667%29%5E%289t%29%29%29 Take the log of both sides



log%2810%2C%282%29%29=9t%2Alog%2810%2C%281.00667%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%282%29%29%2Flog%2810%2C%281.00667%29%29=9t Divide both sides by log%2810%2C%281.00667%29%29.


104.266=9t Approximate the left side


104.266%2F9=t Divide both sides by 9.


11.585=t Divide


So the answer is approximately t=11.585 which means that it takes about 11.585 years for $7,000 to double