Question 1204110
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effective rate = (1 + r/n)^n - 1
effective rate = (1 + 0.04/4)^4 - 1
effective rate = 0.04060401
effective rate = 0.0406


The effective rate is roughly 4.06%


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Another approach


Let's say you deposit $100
We'll calculate the account balance after 1 year when compounding the interest quarterly, at an annual rate of 4%.


A = P*(1+r/n)^(n*t)
A = 100*(1+0.04/4)^(4*1)
A = 104.060401
A = 104.06


Then,
interest = finalAmount - deposit
interest = A - P
interest = 104.06 - 100
interest = 4.06


Divide that interest amount over the deposit to determine the effective rate
effective rate = interest/deposit
effective rate = 4.06/100
effective rate = 0.0406
We get the same value as in the previous section.
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