Converting annual rate of return to quarterly equivalent?

[Carl LaFong]

I am having trouble coming up with a method to convert the annual total
return of an investment to the equivalent quarterly return that would
generate the same final value when compounded 4 times during the year--March
31, June 30, Sept 30, and Dec 31.

Suppose I start the year with 10,000 dollars and end the year with 11,000
dollars. The annual rate of return, compounded annual growth rate, or
whatever you want to call it is 10%, calculated by (11000/10000)-1=.1, or
10%.

What fixed quarterly rate would I have to earn for each of the 4 quarters to
generate the same 11,000 value on Dec 31, assuming quarterly compounding??
The quarterly ending dollar values (other than for Dec 31) are unknown and
irrelevant for this exercise.

Trial and error on a handheld tells me it's between 2.41% and 2.42% per
quarter, but how do I get there in Excel 2007?

I have fiddled with the Nominal and Effect functions to no avail and can't
see how IRR or XIRR would help. Maybe a mortgage or annuity function, about
which I am clueless?

Thanks for any help.

Carl

 

[vezerid]

I am having trouble coming up with a method to convert the annual total
return of an investment to the equivalent quarterly return that would
generate the same final value when compounded 4 times during the year--March
31, June 30, Sept 30, and Dec 31.

Suppose I start the year with 10,000 dollars and end the year with 11,000
dollars. The annual rate of return, compounded annual growth rate, or
whatever you want to call it is 10%, calculated by (11000/10000)-1=.1, or
10%.

What fixed quarterly rate would I have to earn for each of the 4 quarters to
generate the same 11,000 value on Dec 31, assuming quarterly compounding??
The quarterly ending dollar values (other than for Dec 31) are unknown and
irrelevant for this exercise.

Trial and error on a handheld tells me it's between 2.41% and 2.42% per
quarter, but how do I get there in Excel 2007?

I have fiddled with the Nominal and Effect functions to no avail and can't
see how IRR or XIRR would help. Maybe a mortgage or annuity function, about
which I am clueless?

Thanks for any help.

Carl

(1+x)^4 = (1+0.1) =>
(1+x) = 1.1^(1/4) =>
x = 1.1^(1/4)-1

HTH
Kostis Vezerides

 

[David Biddulph]

=1.1^(1/4)-1
or
=POWER(1.1,1/4)-1

 

[Carl LaFong]

Thanks to both of you for the quick response. I have rarely used the Power
function and likely would never have figured it out.


Carl