Joe Boylan Case Scenario - Income Yield and 10 Year period option

I saw a few people asking the same question in the forum, but I still don’t get to understand the concept

So the longer we live, the lower the income yield. Viceversa is we are living less, we will receive a higher income yield

Now, why would you say that by adding a 10-year period certain option to your annuity, your income yield would be reduced when compared with not having the option, but it would be reduced by greater amounts the longer you wait to purchase the annuity?

My thought process is for purchasing the 10 yr certain option, you are buying sort of ‘low risk’ product hence the yield that you will get is definitely lower. If you bought the annuity at a older age, say 70s, the premium u paying is definitely more than when you are in your 30s.

Not sure if it answer your qns? Happy to hear from others as well.

Let’s say that a 60 year old buys ‘life + 10-year period certain’. He is expected to live till 90. Unfortunately, he dies after 1 year. Annuity-seller needs to make payment for additional 9 years instead of 29 years. It seems like a good deal for annuity-seller. Probability of using that ‘period certain’ option is very low if annuitant is young. Risk is there but not by much; hence, income yield in ‘life + period certain’ annuity is slightly lower than ‘life only’ option

Second case -

Let’s say that a 90 year old buys ‘life + 10-year period certain’. He is expected to live till 100. Unfortunately, he dies after 1 year. Annuity-seller needs to make payment for additional 9 years along with the payment for that year 1. So, total 10 payments. Had he died at the age of 100, there would still be 10 payments. So, there is no benefit to annuity seller in this case. That is why income yield is reduced by greater amount if you buy period certain at a later age. In this case, ‘life-only with 10 year period certain’ will work as a ‘Life only Joint’.

Life only for 90 year old male = 20.10
Life with 10 year period certain for a male = 10.66
Life only joint = 14.51

So, the delta is not ~ 10 (20.1 - 10.66) but ~ 4 (10.66 - 14.51) only. Some cost will also incur due to administration and due to the transfer of the annuity.

Overall, it looks like it is better to get ‘life only joint’ when you are old compared to ‘life + period certain’.