j=6.50%
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"???
Same 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.
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.
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%
Thnx Reiny,it is very clear to me.now i can continue the rest which has the similar questions.thnx mathmate too:)
To find the annual interest rate (j) when given the effective interest rate (f) and compounding frequency (m), you can use the following formula:
j = (1 + f/m)^m - 1
Let's apply this formula to the given values:
j = (1 + 0.0325/4)^4 - 1
j = (1.008125)^4 - 1
j = 1.033459 - 1
j = 0.033459
j = 3.35%
Therefore, the annual interest rate (j) is 3.35%.