SOLUTION: [A=P(1+r/n)^nt] Amount invested: $12,500 No. of compounding periods:4 Annual interest rate: 5.75% Accumulated amount: $20,000 Time t in years?

Question 471320: [A=P(1+r/n)^nt]
Amount invested: $12,500
No. of compounding periods:4
Annual interest rate: 5.75%
Accumulated amount: $20,000
Time t in years?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the compound interest formula

Plug in , , (the decimal equivalent of 5.75%), 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 4 to isolate "t".

Divide.

Rearrange the equation.

So it will take about 8.23 years

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