Reverse mortgage math?

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%.
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.
Reply to
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 situations.
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).
======================================= MODERATOR'S COMMENT: A reminder to all posters: Please trim the post you respond to and try to be as succinct as possible.
Reply to
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 --
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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 years" (surprise!).
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 ages:
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 into account.
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 reverse mortgages.
Reply to
Apologies for telling you what you already knew. I got a bit carried away.
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.
Reply to
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.
Reply to
bo peep
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 exhausted.
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.
Reply to
Default User
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 calculator shows these options: single lump sum advance, credit line, monthly loan advance, or any combination.
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Reply to
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.
Reply to
Yes. And taking this one step further, I believe the following is how lump sum is determined.
First, the lender estimates the future value of the home at the end of the term of the loan or life expectancy, based on some expected appreciation rate (or depreciation rate, post-bubble ;->).
Second, the lump sum is the present value of the future home value over the term of the loan or life expectancy, based on a required rate of return (interest rate).
Finally, a monthly payment can be computed based on the lump sum, interest rate, and term of the loan or life expectancy.
Of course, that is very general. For example, in the first step, I suspect that Fannie Mae reverse mortgages use 40% of the current home value to estimate the future value. (As I said, I read that somewhere, but I cannot confirm it now.)
But that paradigm seems to fit the results of two calculators -- not exactly, of course, but in the general vicinity. The varying assumptions (home value v. 40%; and simple life expectancy v. actuarial) seems to explain the very different results of two calculators. The calculators are and Their results, based on an current home value of $350,000, are: age 70: $197,000 lump sum age 80: $236,000 lump sum age 90: $237,000 lump sum age 62: $27,197 lump sum; $426 monthly age 70: $61,983 lump sum; $486 monthly age 80: $133,140 lump sum; $1152 monthly age 90: $200,232 lump sum; $1924 monthly
Thanks for helping me to clarify these ideas. If anyone thinks that I am completely off-base, I'm still listening. But again, the paradigm above seems to fit the data "close enough for government work".
Reply to
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
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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.
Reply to
bo peep
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.
Reply to
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 a while...
Reply to
bo peep
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.
Reply to
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.
Reply to
bo peep writes:
Kiplingers reported a couple of times over the last year of situations where folks who didn't really understand the risks were being convinced to take out reverse mortgages and use the proceeds to buy high-commission insurance products like variable annuities.
This is a nice overview of some of the ways that reverse mortgages are used, as well as a few caveats - things to look out for (ie. potential impact on Medicaid, etc):
Very succinct explanation.
Reply to
BreadWithSpam writes:
PV of an annuity. Standard function on any financial calculator.
PV = 50,000 i = 0.5 (6/12) n = 120 (12*10) PMT = 0 FV = ?
Same function, only the payments are the $50,000 broken down into 120 pieces instead of $50,000 up front as the PV:
PV = 0 i = 0.5 n = 120 PMT = 416.6667 (50,000/120) FV = ?
Then, in both cases, the FV is the combination of the principal *and* the interest owed, so subtract out the $50,000 and you get your $40969 and $18283.
It's not quite that straightforward. There's a formula which varies the percentage by several factors including the age of the borrower, the interest rate, etc. For a 65 yr old borrower, the limit might be as low as 20% or so, while for an 85 yr old, it might be as high as 60%. They have to take into account the fact that they will be owed not just the principal but the interest, too, so the factors for ages vary with the rate of interest as well.
I don't know where to find the HUD table (or if it's actually different from the SSA one).
They factor in lender costs, interest rate *and* age.
Play with that PV function to see how huge a difference interest rates make.
Reply to
Don writes:
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 for).
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.
Reply to
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?
Reply to
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.
Reply to
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.
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