J&S for Money Purchase Plan

I had been asked to calculate the 50 J&S for Money Purchase Plan participants. I did not find any actuarial equivalent provisions in the plan document. What mortality and interest rate should I use? 

What specifically does the document say about the 50 J&S Option?

The monthly annuity shall be provided through an annuity contract purchased by the Plan from a licensed insurance company. This is all I found regarding this matter. 

All you can do is estimate it in a reasonable manner, and clearly explain that it is only an estimate, and that final numbers will be based on final market rates.

One option for an estimate would be to use this site, which I have used for years for rough estimates:    https://www.immediateannuities.com/

In a DC plan you can't self-annuitize, so as Andy mentions, the insurer you prudently choose gets to control those factors.

Thank you. I never deal with DC plans in that matter before. 

I've never had anyone opt for an annuity but have needed to provide the estimates before.  One "comforting" tool is the Schwab Income Annuity Estimation at

https://www.schwab.com/public/schwab/investing/accounts_products/investment/annuities/income_annuity/fixed_income_annuity_calculator

Actually both of these sites calculate Joint & 100% but neither appear to calculate Joint & 50%.

If the site will give you single life APRs and a 100% J&S APR, you could use those to calculate the 50% APR.

Just let me dust off my life contingencies notes here ...

Ax = Single life APR for life aged x
Ay = Single life APR for life aged y
Axy = Joint life APR for lives aged x and y

100J&S = Ax + Ay - Axy

Axy = Ax + Ay - 100J&S

50J&S = Ax + 0.5*(Ay - Axy)
      = Ax + 0.5*Ay - 0.5*[Ax + Ay - 100J&S]
      = Ax + 0.5*Ay - 0.5*Ax - 0.5*Ay + 0.5*100J&S
      = 0.5*Ax + 0.5*100J&S
      = 0.5*(Ax + 100J&S)

So, take your primary annuitant's single life APR, add the 100% J&S APR, and divide that by 2 and you should get the 50% J&S APR. I spot checked this with a few randomly selected ages and mortality/interest assumptions from my software.