# Annuity insutance

Hi All, I am currently reading about insurance and annuities. This is for topic 32.4 on book 4 of the schweser books if anyone is using these. In here it says a statement " The premium paid to the annuity is the price of the annuity. However the convention is to keep the premium constant and adjust the stated annual payout. This means that a lower/higher quoted payout to the annuitant is equivalent to a higher/lower price for the annuity."

Question is why would a lower premium for the annuity generate a higher payout? If I am paying a lower premium then I can only expect a lower payout (I.e. return) on this premium right? What am I missing in my understanding?

I’m really thrown by this wording too. Does the LIII source material state it this way as well?

If you hold the premium constant, then one way to raise(lower) the payout is to raise(lower) the pricing interest rate.

Suppose that you pay a fixed USD 150 per month for a payout of USD 1 million.

If the premium for a payout should actually be USD 140 per month (a lower premium), then your payment of USD 150 per month should give you a payout of USD 1,071,429 (a higher payout than USD 1,000,000).

I think I understand what Schweser is trying to explain:

Let’s say you’re looking for an annuity from a life insurance company for an initial premium of \$100,000. Further, let’s assume the following monthly income quotes from teh interwebz:

Co A \$800
Co B \$820
Co C \$790

If we divide the premium by the quoted income, we get the “price” of the annuity per \$1 of monthly income. Using this approach, Co B has the cheapest “price” of \$121.95, while Co C has the most “expensive” price of \$126.58.