Question 526658: Kayla currently has an account balance of $2,134.96. She opened the account 12 years ago with a deposit of $1,327.35. If the interest compounds twice a month, what is the interest rate on the account?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! If the interest rate had been advertised as 2.4% annually, the interest for half a month would be 1/24 of that or 0.1% of the balance. At the first interest point, they would have added 0.1% of $1,327.35,
to the original $1,327.35, for a balance of
If the interest added per half month (expressed as a decimal)is  ,
each half month the balance gets multiplied by  ,
and after 12 years (144 months), it has been multiplied 288 times, so
From there, I calculate (I used logarithms, not sure how you were expected to solve it)
 and
 , meaning that for one year (24 interest periods), the interest rate would be
The interest calculated is 3.96%.
Spreadsheet software has various functions that would allow to calculate the answer too, even if you did not understand the mathematics behind it.
Probably 4% was meant.
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