SOLUTION: 1) How long will it take for $5000.00 to grow to $15,000.00 if the annual interest rate over that time is 4.85% and continuous compounding is used?

Question 133494: 1) How long will it take for $5000.00 to grow to $15,000.00 if the annual interest rate over that time is 4.85% and continuous compounding is used?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Plug in , ,

Take the natural log of both sides

Break up the natural log on the right side

Subtract from both sides

Rewrite the right side using the identity

Evaluate to get 1

Multiply

Divide both sides by 0.0485 to isolate t

Using a calculator, we get

So it takes about 22.65 years for $5000.00 to grow to $15,000.00
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