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Question 871285: if $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, after how long will the two accounts have the same balance?
4000(1.03)^t=2000(1.05)^t
this is how I set up the equation, is this correct? I am not sure what I am doing wrong, I think I may be applying the wrong principle to solve this, how would you go about it?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! if $4000 is deposited into an account paying 3% interest compounded annually and at the same time $2000 is deposited into an account paying 5% interest compounded annually, after how long will the two accounts have the same balance?
4000(1.03)^t=2000(1.05)^t
this is how I set up the equation, is this correct?
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That's right. Solve for t
4000(1.03)^t=2000(1.05)^t
2(1.03)^t = (1.05)^t
log(2) + t*log(1.03) = t*log(1.05)
log(2) = t*log(1.05) - t*log(1.03)
log(2) = t*(log(1.05) - log(1.03))
t = log(2)/(log(1.05/1.03))
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