Actuarial Interest Rate Formula in F5500

[VeryOldMan]

The following formula is provided for computing interest rate for Form 5500:

i = 2 x I/( A+B-I),

where i= effective rate of return, I= total interest or net gain/loss  A=Beginning Balance, B=Ending Balance.

It seems to work fairly well but can't find the source or prove it myself. Has anyone else looked into this?

[C. B. Zeller]

I assume you're talking about the actual rate of return (used to adjust the credit balances)? The effective interest rate is based on the funding target and has nothing to do with plan assets.

Let's simplify your formula a little. Ending balance B = Beginning Balance A + contributions - distributions + gain/loss I.

I am also going to use r for rate of return because it's confusing to have two different "I"s in the formula, and I am easily confused!

r = 2 * I / (A + (A + contribs - distribs + I) - I)

r = 2 * I / (2 * A + contribs - distribs)

r = I / (A + 1/2(contribs - distribs))

This is just the formula for a dollar-weighted rate of return using simple interest and assuming that all contributions and distributions are made exactly in the middle of the year.

Personally I would not use this unless it would be reasonable under the circumstances to assume that all contributions and distributions happened in the middle of the year (or were made evenly throughout the year). But even then, it's easy to use actual dates and get a more accurate value.

I will point out that if you are currently using this formula, changing it would likely constitute a change in funding method, which would require IRS approval. However it might be eligible for automatic approval under Rev Proc 2017-56.

[C. B. Zeller]

Apparently your formula is known as the "Simple Dietz Method"

https://en.wikipedia.org/wiki/Simple_Dietz_method