I am curious about the math of reverse mortgages. I have done a
google search and looked at some sites, but I cannot find anything
that makes it clear to me.

Disclaimer: I am __not__ considering a reverse mortgage. So I do not
need advice. This is really just an academic exercise for me.

From what I can tell, it appears that there is a lot of smoke and
mirrors that lenders employ to determine the parameters of a reverse
mortgage. Let's not go there.

Assume that the lender has determined that the home equity is
$500,000, the applicable life expectancy(s) is 30 years, and the
lender is willing to pay interest at 5%.

Would the nominal monthly annuity (paid by the lender to me) be
simply:

=pmt(5%/12, 30*12, -500000)

And if I dispose of the property (or die) in 15 years, would the
equity to be paid to the lender be:

=500000 - fv(5%/12, 15*12, pmt, -500000)

In any case, how is the lump sum payment (to me) from the lender
determined?

I presume it's the PV of something. But what?

I have a lot of other questions that go beyond the math. For example,
it's not clear to me why a lender would offer a reverse mortgage. How
is the lender making money in the meantime before the sale of the
property?

Presumably, that "cost of capital" is factored into how the lender
chooses that the interest rate that the lender offers. But even that
math is less clear to me for reverse mortgages than for so-called
"forward" mortgages. I stumbled across an excellent book once that
explained all this. But, sigh, I don't remember the book title.

Anyway, these questions make me suspect that I have the wrong model
for the reverse mortgage, in the first place.

Any help with understanding the mechanics of reverse mortages from
both sides would be appreciated.