I’ve blanked and the search engines are spewing financial reports for my queries.

What’s the equation to convert an annual percentage rate, say 12%, to a quarterly (or semi, or monthly) percentage?

Thanks.

I’ve blanked and the search engines are spewing financial reports for my queries.

What’s the equation to convert an annual percentage rate, say 12%, to a quarterly (or semi, or monthly) percentage?

Thanks.

Well, if the interest is paid monthly and compounded, it’s:

(1 + [sup]x[/sup]/[sub]100[/sub])[sup]12[/sup] = 1.12

So x would be (1.12 - 1)[sup]1/12[/sup] x 100

Er, I think.

You might need a scientific calculator, to calculate that 12th root… (1/12 = 0.08333…)

If you have a compounded annually rate **r** and want to convert it to or from some equivalent interest rate **I** compounded **P** times a year:

r = [1 + (I/P)][sup]P[/sup] - 1

So 12% compounded annually, for example would be equivalent to about 11.49% compounded quarterly.

Is that what you’re looking for?

Sorry, getting confused with all the VB code. That should be:

monthly percentage rate = {(1.12)[sup]1/12[/sup] - 1} x 100 (assuming APR is 12%).

More generally, where M is the monthly rate and A is the APR:

M = {(1 + [sup]A[/sup]/[sub]100[/sub])[sup]1/12[/sup] - 1} x 100

And I *think* (although it’s getting late and my head is hurting) that this would also work for interest compounded at other intervals, as **Cabbage** posted:

Where M is the rate per time interval of [sup]1[/sup]/[sub]T[/sub] of a year, and A is the APR:

(1 + [sup]A[/sup]/[sub]100[/sub]) = (1 + [sup]M[/sup]/[sub]100[/sub])[sup]T[/sup]

==> M = {(1 + [sup]A[/sup]/[sub]100[/sub])[sup]1/T[/sup] - 1} x 100

(NB this assumes A and M are quoted as whole figures, hence the division by 100 to convert the “percentage” interest rate to a fraction")

I notice that **Cabbage** used the term “11.49% compounded quarterly” to mean an overall annual rate of 11.49%, but compoounded each quarter. I’d call that a rate of somewhere under 3% (roughly - I haven’t done the math) per quarter, but I guess it’s all a matter of semantics.

Similarly, a rate of around 0.9% (very roughly) per month will yield an APR of 12%.

Any accountants in the house?