SOLUTION: Sandy is tracking the performance of one of Atlantic Cycles' savings accounts. $10,000 was deposited into this account which earns 2.25% interest compounded continuously. How many

Question 1032586: Sandy is tracking the performance of one of Atlantic Cycles' savings accounts. $10,000 was deposited into this account which earns 2.25% interest compounded continuously. How many years will it take until the account balance doubles if no withdrawals or additional deposits are made?

I set up problem as: $20,000= $10,000*2.718281828459(.0225x). I got 32 years as answer but this was wrong. Please help. Thank you.
Found 2 solutions by LinnW, MathTherapy:
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
It should be $20,000= $10,000*2.718281828459^(.0225x)

Using www.wolframalpha.com for the calculation,
we get x = 30.8065
Using wolfram again for 10000*2.718281828459^(.0225*30.8065)
we get 19999.98138881
Finally lets check 20000 = 10000*2.718281828459^(.0225*x)
This also produces x = 30.8065 as well
I hope this helps.

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Sandy is tracking the performance of one of Atlantic Cycles' savings accounts. $10,000 was deposited into this account which earns 2.25% interest compounded continuously. How many years will it take until the account balance doubles if no withdrawals or additional deposits are made?

I set up problem as: $20,000= $10,000*2.718281828459(.0225x). I got 32 years as answer but this was wrong. Please help. Thank you.

Future value (A), and present value (P) amounts are INSIGNIFICANT, so they don't have to be used.

Doubling means that A = 2P. We then get:

------ Substituting .0225 (2.25%) for r
----- Converting to LOGARITHMIC (natural) form
t, or time =
Note that 30.80654 is NOT THE SAME as 32 years. Even if it were requested that time be rounded to the nearest year, it'd be 31, not 32.
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