Same as your example, but solve for j.
In your example, n=365, and in this case n=4 (quarterly).
You can solve for j by taking the fourth root on both sides (square-root twice) to get
1+j/4 = fourth-root(1.0325)
the rest is standard algebra.
Looking at your procedure, I conclude that you are finding the equivalent annual rate for a given rate compounded daily.
I don't like the way you are writing it up. You are writing down steps connected by equal signs when they are not equal.
the second and third lines are NOT equal. This may sound picky to you, but math is exact.
I used to teach it this way:
let the annual rate be i
(1 + i = (1 + .065/365)^365
1 + i = 1.067152848
i = .067152848
effective annual rate = 6.72%
for your last question, I will assume that it asked the following,
"What annual rate compounded quarterly is equivalent to an annual rate of 3.25%
Let the quarterly rate be j
1.0325^1 = (1+j)^4
take the 4th root of both side
1.0325^(1/4) = 1+j
1.008027813 = 1+j
j = .008027813
4j = .032111251
the annual rate compounde quarterly will be 3.211%
Thnx Reiny,it is very clear to me.now i can continue the rest which has the similar questions.thnx mathmate too:)