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October 1, 2014

Posted by **Amy** on Saturday, March 27, 2010 at 5:36pm.

m=Daily(365)

f(effective rate)=?

f=(1+i)^n

=(1+(.0650/365))^365

=1.067152848-1

=0.067152848

=6.72%

i know how to find the "f"

but if its

j=?

m=Quarterly(4)

f=3.25%

how do i find the "j"???

- math help plz! -
**MathMate**, Saturday, March 27, 2010 at 6:33pmSame as your example, but solve for j.

In your example, n=365, and in this case n=4 (quarterly).

f=(1+j/n)^n

f=(1+j/4)^4

1.0325=(1+j/4)^4

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.

- math help plz! -
**Reiny**, Saturday, March 27, 2010 at 6:40pmLooking 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.

e.g.

f=(1+i)^n

=(1+(.0650/365))^365

=1.067152848-1

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

then

(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

then ...

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%

- math help plz! -
**Amy**, Saturday, March 27, 2010 at 6:59pmThnx Reiny,it is very clear to me.now i can continue the rest which has the similar questions.thnx mathmate too:)

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