Question 1204110: A savings association pays 4% interest compounded quarterly. What is the effective
annual interest rate? Found 2 solutions by Theo, math_tutor2020:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! growth rate per year = 4% / 100 = .04.
growth rate per quarter = .04/4 = .01.
growth factor per quarter = that + 1 = 1.01.
effective growth factor per year = 1.01 ^ 4 = 1.04060401.
effective growth rate per year = that - 1 = .04060401 * 100 = 4.060401% per year.
that's the effective annual interest rate when the annual innterest rate is compounded quarterly.
You can put this solution on YOUR website!
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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