Ever wonder where your money goes?

[plural]

I'm the first to admit that most of what I post here
while entertaining, amusing and perhaps even insightful
isn't really all the important to your daily lives

but, ernunnos posted this video and you really need to watch it

Comments

[budhaboy]

Heh.

Using wikipedia, and verifying the following using Excel, I get:

n=Ln(((1+i)^N-1)/f+1)/Ln(1+i)

Where:

i=annual_interest/number_periods_in_compounding
N=Number_of_periods
n=number_of_periods_to_payoff_with_payment=f*A
A=payment_as_normally_computed
f=some_factor

So, if you have f=1, you'll get n=N

If you use f=13/12 (i.e. making 13 payments of size 'A' for each payment of size f*A... the number you suggested) on a 30 year mortgage (N=360), and APR=0.05 (i=.004167) you'll get:

n=345.1943, or 28.76619 years.

NOTE: this payoff time is dependent not only on the factor, but the original number of periods, and the interest rate. IF the apr goes up (to say 15%), n=353.6322... If the apr stays at say 0.05% and N drops to say 180 (15 year mortgage), n=170.0494

It's funny, because I've always heard something like what you'd suggested, but it was always, like 'an extra payment will take five years off... or if you double it, you'll halve length of the mortgage (in point of fact, doubling the payment on a 30 year fixed at 5%APR lowers the time to payoff to 241.8751... not even 10 years!) it seemed reasonable, but your number seemed way off and prompted me to actually work it out... I'm sort of stunned actually how little it actually matters...

As always, check my work brother as I'm actually a slack-jawed moron.

[budhaboy]

Definately a slack-jawed moron...

I just noticed the 'nper' function in excel... If I'm applying it correctly, 13/12 a 'normal' payment grinds out to 310.7826 (about 25.8 years)... saving you just over four years... I'm not sure why my formula isn't correct, and I've tragically lost interest as it's way closer to my conventional wisdom would say...

Again, there's no guarantee I'm doing any of this right as I've just proven, I'm a slack-jawed moron.

[plural]

Nope, you are doing it correctly, I just didn't give you the correct set of parameters as it had been three years since I did the calculations myself.

Once I had the calculator in front of me and started actually modelling the terms of my original loan, I realized that I was overpaying by more than just an extra payment and that the contrast between my interest rate (high) and loan amount (low) put my particular situation into the outlier realm, particularly when you add in how much I was overpaying.

[budhaboy]

One could argue though that if you were able to earn better than your interest rate over the course of the loan, you'd be better off applying that stream of payments to the higher yield, as at the end of the day, you'd have more money in the coffers. The only thing is, it's easier to guarantee making a larger payment than it is you'll be able to guarantee a high rate of return...

Tragically in my case, I'm not convinced I could do better than mortgage interest.

Do you remember our former realtor/neighbor? The one who was trying to convince me to go interest only on the mortgage, then faithfully put principle payments into a moneyfund, and make the interest payments on the loan?

She hasn't sold a house in two years, and really, really coming to regret her decision to do so.

[plural]

Actually, its pretty interesting.

Assume you have a 30 year fixed rate mortgage with a inital balance of $100,000.

From that point we examine two possible scenarios:

1) you deposit $2400 into an investment account once per year earning X% return for 30 years

2) You have a mortgage at rate Y% and you pay down your mortgage by an extra $200 per month and when your mortgage is paid off, you invest the same amount you have been paying for your mortgage in an investment account which earns the same X% for the remainder of the 30 year period.

If X = Y and Y = 5% then Scenario 2 nets a profit of $2,174.06

However, you only have to increase X to 5.13% before the value of Scenario 1 exceeds Scenario 2 (if only by $162.67).

Of course, then the question becomes is it worth the risk of the investment?

As long as you intended to stay living in the house, there is 0 risk in paying down the mortgage early and significantly less aggregate risk (because you are risking a smaller portion of your overall earnings) in the investments once the mortgage is paid off as you've already taken profits of just over 45k in the form of interest savings.

So the question becomes how much greater does X have to be than Y before it makes sense to take the additional risk.

Well, Lets see what values we get for P (profit) by representing the difference between X & Y with the variable Z (stated as X = Y+Z):

As I've already shown:

if Z = 0% then P = -$2,174.06
if Z = 0.13% then P =$162.67

Not exactly a stellar improvement over 30 years

if Z =0.5% then P = $7,316.82

Better but again only an annual difference of $243.89

if Z = 1.0% then P = $18,269.11 or $608.97 per year

If Z = 1.5% then P = $30,867.38 or $1,028.91 per year

Ok so at Z = 1.5% we are atleast at a sizable chunk of change but still questionable if it compensates for the risk.

if Z = 2% then P = $45,317.67 or $1,510.59 per year
if Z = 3% then P = $80,722.25 or $2,690.74 per year

At this point we're definitely in the territory of it being worthwhile, however we also have to recognize that as we make Z larger, the risk involved in the investments goes upsignificantly and becomes more difficult to obtain.

Given that Z = 3% is equal to a rate of return of 8%, that is pretty much pressing your luck for the risk adverse investments. To reliably earn rate of 8% or higher you are going to have to include some investment vehicles with significantly higher volitilaty.

Of course, getting an 8% return on a year isn't hard, nor is getting it for a few years in a row, but that is an entirely different matter than doing it for 30 years in a row.

I'd be hard pressed to think that you really could reliably outperform the value obtain through an accelerated payoff of your mortgage through conventional investment portfolios.

If you had your own business, I'd say you'd have a fair chance of significantly outperforming Y by investing that money into your business (assuming you are a competant business person) but then again, given the risk inherent in small businesses, I would think you would be better served by offsetting or dampening that risk by paying off your mortgage.

[budhaboy]

I'm also of a mind that it isn't entirely about profit... you need to have fallback positions of security. Since you live in your house it should be the asset of last resort, and as such you shouldn't leverage it unless you absolutely have to (i.e. most people when they purchase it).

It's a shame about Anne, but what are you going to do? I tried to warn her... she gave me a knowing look of someone who'd drank deeply from the kool-aid, and know amount of her cajoling would ever enable me to 'get it.' Shame on me, I guess...

[plural]

Agreed.

The most valuable thing you can buy with money is the security of knowing someone can't take your house from you or your ability to feed yourself.

If you can do those two things, all of life's other problems are manageable.

Yeah, I hate to see nice people suffer (my vague recollections of her was that she was decent people) but what can you do, everyone thinks they can outsmart the system then all they see is gold and you'll never convince them otherwise.

Of course, her situation kind of reminds me of that century 21 ad from a couple of years ago.

"Honey, it will be ok, Suzanne researched this"

I have to wonder how many people took advice like Anne and other agents were giving and are now wondering how they got gravel in their vaseline.

[plural]

Do you remember our former realtor/neighbor?

I do although it hadnt crossed my mind till you brought her up.

Yeah, she has to be hurting something fierce right now.

Its funny, how when it comes down to it, getting fancy with your money is always bites you in the ass.

When I went to buy Bettie, I had the cash on hand and was going to pay cash for her. My broker at the time convinced me to take out a motorcycle loan at 5.5% through my credit union and leave the money in the market.

Yeah well, 6 months later the market tanked and the money I should have spent on the Duc was lost about 25% of its value and I had a loan to pay.

Of course, I was at MSFT and making bank at the time so I didn't worry about it and by the time I liquidated my US stock positions in Dec 01, my portfolio has recovered so I was able to pay off the loan early and get out from under a stupid decision relatively cheap.

Now days, I don't care what the upside is, I'd rather know that my assets are protected from involuntary alienation than make a few extra bucks.

As I said at the end of my previous comment, I have enough risk in my professional/business life, I don't need to augment it with debt or financial risk in my personal life.

[lumiere]

This is kinda simplistic.

Both here and below you can improve the models by including the tax implications (at least for US taxpayers, which I presume you are). Tax effects don't affect the overall feel of the space, but they do change the details, and particularly where the break-even point is in practice.

To summarize, for most US taxpayers:
* interest paid on a home mortgage is tax deductible
* investment income is taxed and/or illiquid (e.g., in an IRA)

Additionally, you should consider buying equity in the home as buying insurance against other financial woes (as it can be tapped via home equity loans), and the risks involved in failing to diversify investments outside of home equity (as the recent fail in home prices demonstrates).