Joint & Survivor with 10-year Certain

[JAY21]

Anyone able to illustrate the general structure of building the annuity factor (in general) for a 100% Joint and Survivor Annuity with a 10-year certain feature. Either with first principles or commutation functions. I've never run across this annuity combination before.

[david rigby]

Basic principles:

- Create a 100% J&S at (current ages + 10).

- Discount this by 10 years interest, and 10 years of survivorship for both.

- Add a 10-year certain.

If you have varying interest rates, the algebra is more complex, but same structure.

Something like:

a(angle 10) + v^10 * 10px * 10py [N(x+10)/D(x+10) + N(y+10)/D(y+10) - N(x+10:y+10)/D(x+10:y+10)]

Please check. I'm rusty w/r/t commutation functions.

[Guest greybeard]

An alternative solution might be something like:

ax+ay+a10-ax:10-ay:10-ax:y+ax:y:10

[SoCalActuary]

Basic principles:

- Create a 100% J&S at (current ages + 10).

- Discount this by 10 years interest, and 10 years of survivorship for both.

- Add a 10-year certain.

If you have varying interest rates, the algebra is more complex, but same structure.

Something like:

a(angle 10) + v^10 * 10px * 10py [N(x+10)/D(x+10) + N(y+10)/D(y+10) - N(x+10:y+10)/D(x+10:y+10)]

Please check. I'm rusty w/r/t commutation functions.

I think not, Dave. Your method assumes that both participants must survive the 10 years before the deferred payment occurs.

This revision reflects the potential that one or the other survives, as well.

a(angle 10) + [N(x+10)/D(x) + N(y+10)/D(y) - N(x+10:y+10)/D(x:y)]

[david rigby]

You're correct. Thanks.