Answer precalculus word problem.

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If u deposit $1,000 into an account that pays 4% interest compounded continulously, how long will it take the account to grow to $2000? 

Please show step by step 

Aug 30th, 2015

Thank you for the opportunity to help you with your question!

The formula used with continuous compounding interest is: 
A = Pe^rt 
we are given A, P and r: 
2000 = 1000e^0.04t 
divide both sides by 1000: 
2 = e^0.04t 
take Napierian log of both sides: 
ln2 = 0.04t 
divide both sides by 0.04: 
t = ln2/0.04 ~ 17.33 years or 17years 4 months 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Aug 30th, 2015

isnt it 1.04 instead of 0.4 since it is interest? 

Aug 30th, 2015

Hi,

     You can take it as plain interest in terms of compound interest. So it is just 4/100=0.04.

Aug 30th, 2015

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