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Answer:
<u>2.53%</u>
Explanation:
We need to understand what effective annual rate is to solve this question.
Effective Annual Rate is the actual interest earned on an investment due to effect of compounding.
The formula is:
Effective Annual Rate =
Where
i is the interest rate given (nominal interest rate)
n is the number of compounding per year
For the old bank,
5% is the interest rate, so i = 5% = 5/100 = 0.05
n is the number of compounding per year, that will be n = 12 since compounding monthly
So, we have:
Effective Annual Rate
For second bank, we have:
i = what we need to find
n = 2 (since semi annual compounding, every 6 months)
So,
Effective Annual Rate =
This should be equal to APR from 1st bank (0.05)
So, we solve for i:
So, the interest would have to be
0.0253 * 100 = <u>2.53%</u>