SOLUTION: Hello: I have a problem I cannot seem to solve. I am hoping you can help me solve it or point me in the right direction. I am trying to solve the compound interest formula for the

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Question 438977: Hello:
I have a problem I cannot seem to solve. I am hoping you can help me solve it or point me in the right direction. I am trying to solve the compound interest formula for the time variable; however my memory of log is very shady. What I need is:
given a starting dollar amount
a fixed monthly deposit
and a fixed interest rate
I want to know how long until the balance reaches X amount?

the original formula that solves for final balance is
B = A(1+i)^N + (P/i)[(1+i)^N − 1]

B = ending balance
A = starting balance
i = monthly rate
P = monthly deposits
n = how many months

thanks in advance!

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
B = A(1+i)^N + (P/i)[(1+i)^N − 1]
Solve for "N":
A(1+i)^N + (P/i)(1+i)^N = B+1
-----
[A + (P/i)](1+i)^N = B+1
---
(1+i)^N = (B+1)/[A+(P/i)]
---
Take the log of both sides:
N*log(1+i) = log[(B+1)/((Ai+P)/i)]
----
N = {log[(B+1)/((Ai+P)/i)]}/log(1+i)
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Cheers,
Stan H.
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