SOLUTION: Anne deposits $2500 in an account that earns 7.5% annual interest compounded quarterly. Find out how long it will take for Anne to earn $500 in interest

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Question 255702: Anne deposits $2500 in an account that earns 7.5% annual interest compounded quarterly. Find out how long it will take for Anne to earn $500 in interest
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
Remember that the formula for compound interest is:
A+=+P%281+%2B+r%2Fn%29%5Ent
In this problem, P = 2500, r = 0.075, n = 4 and t is our unknown. If Anne earns $500 in interest, then the total amount she has is A = 3000. So our problem is:
3000+=+2500%281+%2B+0.075%2F4%29%5E%284t%29
Our first step is to divide both sides by 2500.
1.2+=+%281.01875%29%5E%284t%29
Now, we need to get the exponent down since that is where the variable is. So we take the log of both sides:
log%281.2%29+=+%284t%29log%281.01875%29
Now we divide both sides by log(1.01875):
log%281.2%29%2Flog%281.01875%29+=+4t
And last, we divide both sides by 4:
log%281.2%29%2F%284log%281.01875%29%29+=+t
Using the calculator, we have that t = 2.45 years.