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?

Algebra ->  Rational-functions -> 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?      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
A=Pe%5E%28rt%29 Start with the given equation


15000=5000e%5E%280.0485t%29 Plug in A=15000, P=5000, r=0.0485


ln%2815000%29=ln%285000e%5E%280.0485t%29%29 Take the natural log of both sides


ln%2815000%29=ln%285000%29%2Bln%28e%5E%280.0485t%29%29 Break up the natural log on the right side


ln%2815000%29-ln%285000%29=ln%28e%5E%280.0485t%29%29 Subtract ln%285000%29 from both sides


ln%2815000%29-ln%285000%29=0.0485t%2Aln%28e%29 Rewrite the right side using the identity ln%28x%5Ey%29=y%2Aln%28x%29%29

ln%2815000%29-ln%285000%29=0.0485t%2A1 Evaluate ln%28e%29 to get 1


ln%2815000%29-ln%285000%29=0.0485t Multiply


%28ln%2815000%29-ln%285000%29%29%2F0.0485=t Divide both sides by 0.0485 to isolate t


Using a calculator, we get

t=22.6517998


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