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.
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%.
In Excel terms, 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:
P0000 - fv(5%/12, 15*12, pmt, -500000)
In any case, how is the lump sum payment (to me) from the lender
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
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.
On Nov 17, 2:50 pm, email@example.com wrote:
The lender will allow you to accumulate indebtedness up to some
fraction of the home equity. Think of this as a home equity line of
credit where you can only draw down a certain amount each month, and
you do not make repayments until the end (i.e. a baloon payment). In
most cases the baloon payment is made out of the proceeds from the
sale of the property either when the owner dies or is forced to sell
the home to qualify for medicaid funded nursing home care or some
other life change.
The lender has negative cash flow, but positive income in an
accounting sense because the borrowers indebtedness grows by both
interest on past payments and new payments. But the insidious thing is
that reverse mortgages tend to have huge fees because the borrower is
not too concerned about the terms, only the amount they can get for
current consumption (not a value statement, just my experience from
talking to people who are considering this). People are very bad at
figuring out how fast their equity will decrease once they have
received a few years payments.
I have actually seen reverse mortgages in only two types of
1. Cold call, where the lender tries to talk the elderly person into
the mortgage and the borrower doesn't even know the nature of the
transaction. They think that this is some kind of conversion of their
home equity into an investment that is throwing off a yield.
2. Bundled into the sales pitch for something (timeshare, investment
property) that the buyer cannot afford the payments on. First you sell
them something at an inflated price, then you get them to finance it
through an awful financing package.
To return to your original question, the lender structures the deal to
make payments to the borrower in an amount that will not exhaust the
equity until well past the life expectancy of the borrower (or
borrowers if joint owners).
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On Nov 18, 3:02 pm, firstname.lastname@example.org wrote:
Thanks for your response. I was aware of this goal in general terms.
I was looking for specifics of the math involved. For example, a web
page that I found later -- http://www.goldengateway.com/reverse/math.do
-- offers the following example, more realistic than mine.
Suppose we borrow $50,000 over 10 years at 6%. The web page states:
"If you borrow a total of $50,000 over ten years at an interest rate
of 6%, you will owe $40,969 [in interest, in addtion to the principal]
if you take all of the money up front, but only $18,283 if you take
the money in monthly installments".
I wanted to know how $40,969 and $18,283 were computed. I got the
answer in a more technical forum. My formulas were not too far off.
If anyone is interested, I will gladly provide the details.
However, there are still some lingering questions that this forum
might help with.
First, the web page has another example where the nominal maximum loan
amount (before taking life expectancy into account) is the appraised
value of the home, namely $350,000. (Actually the appraised value
reduced by some factors.)
But I thought I read somewhere that for US HUD/FHA-backed reverse
mortgages, the nominal maximum amount is limited to 40% of the
(modified) appraised value.
Is that right? I cannot find that information again at the moment.
Second, using a nominal maximum amount of $350,000, the web page tries
to explain how life expectancy is factored. It says: "The HUD/FHA
amortization table basically subtracts your current age [at least 62]
from 100 years, and divides the maximum loan amount by your expected
life span. The other reverse lenders also factor your age in the same
way, although each one has a slightly different forecast of your
expected life span".
I cannot find the HUD/FHA amortization table online. Can someone
provide a pointer?
(I am content to use the RMD or SSA life expectancy tables, which I
__can__ find. But I'm still interested in seeing the HUD/FHA table.)
In any case, I do not understand "divides the maximum loan amount by
your expected life space". I don't believe it gibes with the example
numbers below, not literally, especially if life expectancy is
determined simply by "subtracts your current age from 100
Finally, taking all that for granted and using a (modified) appraised
value of $350,000, the web page says you can borrow the following
amounts at the various
Age 70: can borrow $197,000
Age 80: can borrow $236,000
Age 90: can borrow $237,000
Do you have any insight into how those numbers were derived?
I know that the derivation can be made difficult (impossible!) to
predict if lender costs are factored in. I don't know if they are.
But hopefully that's a small enough delta that my question can
answered "close enough for government work" without taking those costs
I know there are numerous online reverse-mortgage calculators that
provide the loan amount based on life expectancy. I'm just curious
about the computation behind them, with the understanding that lenders
figure life expectancy differently.
Disclaimer: As I said before, I am __not__ considering a reverse
mortgage. This is really just an academic exercise for me. So I do
not need any subjective advice or commentary about the nature of
On Nov 19, 5:11 am, email@example.com wrote:
Apologies for telling you what you already knew. I got a bit carried
I think this is an actuarial calculation, not a simple division. They
are trying to predict how many years you are likely to keep living
*after* borrowing the maximum amount. During that time you are not
getting any more payments, but you are accruing interest and the bank
needs to be reasonably sure that you will not live so long that you
end up owing much more than the house is worth when you actually die.
On Nov 19, 11:02 am, firstname.lastname@example.org wrote:
Where are you getting this information?
That is *not* how reverse mortgages work - once a payment schedule is
set up, you are supposed to get that exact same payment every month
for the rest of your life, regardless of how long you live. If you
live to 120, the lender will be a major unhappy camper. In reality,
the majority of people who get reverse mortgages end up selling the
house well before they die.
It depends on the type of reverse mortgage. From the HUD FAQs:
10. How do I receive my payments?
You have five options:
* Tenure - equal monthly payments as long as at least one borrower
lives and continues to occupy the property as a principal residence.
* Term - equal monthly payments for a fixed period of months selected.
* Line of Credit - unscheduled payments or in installments, at times
and in amounts of borrower's choosing until the line of credit is
* Modified Tenure - combination of line of credit with monthly payments
for as long as the borrower remains in the home.
* Modified Term - combination of line of credit with monthly payments
for a fixed period of months selected by the borrower.
If televison's a babysitter, the Internet is a drunk librarian who
won't shut up.
With some if not all reverse mortages, you have the option of
receiving the entire principal in one lump sum at the outset of the
loan term. That is the case I assumed "themighty" was talking about.
Source: For Fannie Mae "Home Keeper" reverse mortages, the aarp.org
calculator shows these options: single lump sum advance, credit line,
monthly loan advance, or any combination.
Source: http://en.wikipedia.org/wiki/Reverse_mortgage .
On 2008-11-20 02:05:26 -0800, email@example.com said:
The OP presumably is just interested in the math of reverse mortgages,
and that is fine. But in a newsgroup like this, I should hope that more
people would be concerned about the dangers and pitfalls of reverse
mortgages and whether or not they are suitable for seniors and how they
are subject to abuse, if not in this thread at least in another one
sometime. My understanding is limited, but I have read some discussions
of the topic, and I have yet to encounter what I would call an
"authentic financial planner" (as opposed to a sales person) who
recommends reverse mortgages.
There *have* been some favorable mentions here, generally with some
qualifications added. For example, "The reverse mortgage is often a
godsend for couples who want to stay in their own home, especially if
they've already downsized" in
However, I see even more comments here of "the dangers and pitfalls of
reverse mortgages" type coming from financial planners, but almost
never with specific information.
Yes. I should think that specific information about this topic would be
extremely helpful for seniors considering reverse mortgages. It seems
to me that how to build the equity in one's home and how to use it in
retirement years is a huge part of general lifetime financial planning.
Actually, it isn't even necessary to *use* the equity. In my case, my
mortgage payment is my largest monthly bill, and my main hindrance to
retiring. I would be happy to just stop making the payments while
still living in the house. I don't need to leave it as part of my
estate. Waiting for the housing market to recover... might take quite
I should think that staying in the house and continuing to pay the
mortgage would be far better than selling the house and renting.
Possibly the mortgage payments are less than rent in many areas.
Presumably those mortgage payments come to an end sometime, and then
you have a house and no further payments. All this would depend a lot
on details of how much equity has been built up and many other things,
but in my opinion eventually owning a house free and clear is a big
plus and should be a numbert 1 priority in planning.
I plan to stay in this house for the rest of my life! Even if I keep
paying the mortgage, it's cheaper than renting.
My situation is different - never married, never had any kids, next of
kin would sell the house anyway. I have no incentive to own the house
free and clear if I can live in it for the rest of my life without
making mortgage payments for the next 25 years. (took out a 30 year
fixed mortgage 5 years ago at age 57).
I suspect that I am close to being an ideal candidate for a reverse
mortgage, except that my equity is a bit too low right now.
In a sense, a reverse mortgage is somewhat similar to an
immediate fixed annuity. You get to keep your house for
the rest of your life, but with a good chance that your
heirs will get nothing. If your concern is for your
current quality of life rather than your heirs (especially
if you don't have any or if they are adequately well off
already), arguably, that's a sensible trade.
If you don't need to leave the equity in your house to
your estate, you might as well find a way to spend it
before you die. There are only a few ways to use up
the equity in your home and some of them run a serious
risk that you'll end up without the home but still living.
For example, if you take out a regular mortgage and
spend the cash and end up unable to make your mortgage
payments. Or same for a HELOC. Or if you sell the home
and take the cash to the bank and spend it down while
renting (unless you can somehow guarantee yourself rent
at a rate substantially less than you can buy an annuity
While I'd be wary of most of those choices, and I'd be
wary of spending down one's home equity in general,
it's not necessarily the worst way to do so if you
want to be assured of continuing to live in your house.
Of course, at some point, if all that money gets spent,
there may be real concerns about other ongoing costs
associated with the house - no mortgage payment, and
possibly there will be an opportunity to defer property
taxes, but you still have maintenance and repair and
insurance costs to keep up.
Plain Bread alone for e-mail, thanks. The rest gets trashed.
No HTML in E-Mail! -- http://www.expita.com/nomime.html
On 2008-12-05 07:05:42 -0800, firstname.lastname@example.org said:
Granted that the goals you describe are sensible, are there not other
ways of accomplishing them without an intermediary financial
institution setting up a reverse mortgage?
And, assuming the homeowner could tap the equity in some way, ere there
not other financial products that would give better returns, especially
in future years, than an immediate fixed annuity?
I think entering into a reverse mortgage is like finding a lender of last
resort. It's a desparate act and I agree with BreadWithSpam that the
posibility that a good chunk of the payments you receive will go toward
maintanence and upkeep. Selling the house, especially if it's paid for, can
be a better option for many people. Some people can't let go. If I needed
the funds I would have no problem selling and downsizing or even renting.
Another option that works well for some people is to rent out a couple
of rooms in the big house to tenants. lt's like downsizing, but keeping
the house and getting income from the rentals at the same time. One
variation on this plan is to rent the rooms to a younger person or
couple who will do some work around the house, handyman chores, etc. in
lieu of a part of the rent.
One of my relatives some years back stayed in her own home until she
died and brought in nursing staff and caretakers around the clock to
look after her. It was more cost effective than a nursing home,
although she did live in a part of the country where there were a lot
of casual workers available for rather low wages. I think the plan
would be worth looking into in any location.
With emphasis on "casual," "low wages" and lawbreaking. Many home
health care aides will work for cheap as long as the employer breaks
the law and does not pay the employer's share of social security and
medicare taxes. This helps ensure the low income employee does not get
caught for failing to pay self-employment taxes.
Anyone with so much money they can afford round the clock health care
surely is a bit concerned about his/her reputation as a law abiding
citizen. Plus the typical home health aide really needs to have some
kind of retirement plan, and often this will be solely social
security--assuming they actually pay their self-employment taxes or
their employer pays their Medicare and SS taxes.
On 2008-12-05 14:16:32 -0800, email@example.com said:
No lawbreaking is necessary. As I recall, my relative did make social
selcurity contributions and whatever other payments were required by
state law. All things considered, I would guess she provided more
benefits than Wal-Mart. I suggest that anyone considering this kind of
plan run the numbers and allow for such extra costs. I still believe it
would be more cost effective than a nursing home. There are intangible
benefits like keeping your own home, having more control over your
daily living, and so on. And on the other side of the ledger there are
definitely risks associated with choice of a nursing home and entry
Correct, it is not. However, paying SS and Medicare taxes pushes up
the hourly wage about 9%.
Really? Did she offer a 401(k)? Job advancement opportunities? Health
insurance opportunities? Working at Wal-Mart also has the benefit of
protecting employees' rights through employment law. Your relative
could fire at will. Not so with Wal-Mart.
There is also the reality that keeping good help requires paying more
than what local agencies pay. I have a wealthy relative who did round
the clock health care for a short while until another relative of hers
ran the numbers and found her savings would be wiped out in five years
at the rate she was spending money on home health care. At a very nice
nursing home, the costs were such that she could stay indefinitely.
Round the clock home health care has its advantages, but in my
experience, unless one breaks the law, financial savings generally
will not be one of them.
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