Question 1030872: Suppose you inherit $20,000. You find an investement accunt that pays 5.5% interet compunded continuously. How long will you need to keep it in the account until you have $30,000?
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Let's start with the formula for compound interest
A = Pe^rt
where A is the final amount, P is the principal or initial amount, e is the mathematical constant also known as Euler's number since Euler discovered it, r is the rate and t is the time.
30,000 = 20,000*(e^0.055t)
30,000/20,000 = e^0.055t
1.5 = e^0.055t
log(1.5) = log(e^0.055t)
0.1760 = 0.055t*log(e)
Divide both sides by 0.055
3.20 = t*log(e)
3.2/log(e) = t use your calculator, get log(e) then divide 3.2/the log to get:
7.37 = t
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