SOLUTION: Urgent help please! How long will it take $900 to double itself if it is invested at 10% interest compounded semiannually? (Express the answer to the nearest tenth.)

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Question 457955: Urgent help please! How long will it take $900 to double itself if it is invested at 10% interest compounded semiannually? (Express the answer to the nearest tenth.)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: 900 doubles to 1800





A=P%281%2Br%2Fn%29%5E%28n%2At%29 Start with the compound interest formula


1800=900%281%2B0.10%2F2%29%5E%282%2At%29 Plug in A=1800, P=900, r=0.10 (the decimal equivalent of 10%), and n=2.


1800=900%281%2B0.05%29%5E%282%2At%29 Evaluate 0.10%2F2 to get 0.05


1800=900%281.05%29%5E%282%2At%29 Add 1 to 0.05 to get 1.05


1800%2F900=%281.05%29%5E%282%2At%29 Divide both sides by 900.


2=%281.05%29%5E%282%2At%29 Evaluate 1800%2F900 to get 2.


ln%282%29=ln%28%281.05%29%5E%282%2At%29%29 Take the natural log of both sides.


ln%282%29=2%2At%2Aln%281.05%29 Pull down the exponent using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29.


ln%282%29%2Fln%281.05%29=2%2At Divide both sides by ln%281.05%29.


0.693147180559945%2Fln%281.05%29=2%2At Evaluate the natural log of 2 to get 0.693147180559945.


0.693147180559945%2F0.048790164169432=2%2At Evaluate the natural log of 1.05 to get 0.048790164169432.


14.2066990828905=2%2At Divide.


14.2066990828905%2F2=t Divide both sides by 2 to isolate "t".


7.10334954144523=t Divide.


t=7.10334954144523 Rearrange the equation.


t=7.1 Round to the nearest tenth (ie to the nearest tenth of a year).


Answer: 7.1 years.