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.)

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) (Show Source): You can put this solution on YOUR website!
Note: 900 doubles to 1800

Start with the compound interest formula

Plug in , , (the decimal equivalent of 10%), and .

Evaluate to get

Add to to get

Divide both sides by .

Evaluate to get .

Take the natural log of both sides.

Pull down the exponent using the identity .

Divide both sides by .

Evaluate the natural log of to get .

Evaluate the natural log of to get .

Divide.

Divide both sides by 2 to isolate "t".

Divide.

Rearrange the equation.

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

Answer: 7.1 years.

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