# Math Behind Buying a House

Is following calculation correct?

I spend \$1500/month on average on rent. If I rent for the next 3 years, I would be spending \$54,000.

I can buy a house for \$220,000 today and spend the same amount on the mortgage.

In 3 years, if the market gets soft, and I have to sell the house for \$200,000. Am I still better off than renting, because, \$180,000 (taking off 20k for the realtors and closing costs), less \$220,000 (\$40,000) is still smaller than 54k?

By the way, I am planning to keep the house for about five years. I am making the argument just to be on the safe side.

• Have you factored in property taxes + maintenance + closing costs (both costs on buying the property + selling the property in 5 years)? Commented Aug 28, 2017 at 15:23
• In general, you are better off buying for 5 years then renting. If it is a hot area, you can break even in a shorter time frame. Less if the area is slow. Please consider risk in your calculation. If you can afford to replace a HVAC system then you are okay to buy If not continue to rent. Commented Aug 28, 2017 at 15:26
• The New York Times made a calculator for this you might find useful. Commented Aug 28, 2017 at 17:17
• Three people decide to share a hotel room and pay \$100 each, in cash. The hotel manager realizes that they've overpaid and sends a bellhop with \$50 in tens up to the room. The bellhop pockets \$20 and tells the guests that the room was actually only \$270, and gives them ten each. So the guests paid \$90 x 3 = \$270, the bellhop kept \$20, so that's \$290, but they originally paid \$300, so where did the missing \$10 go? Now do you see why your math is wrong? Commented Aug 29, 2017 at 14:33
• @A.Anand: That's correct. The point of this joke was: you can't just take a bunch of numbers and add them together and compare them. Just as in the joke we computed \$300 - (\$270 + \$20) for no reason whatsoever, so too is the original poster here simply picking a bunch of numbers and adding and subtracting them without any underlying logic to those operations. The question is "my expenses stayed the same, and then I bought something and sold it for less than I paid for it; did I make money?" No, you can't make money by selling something for less than you paid for it. Commented Aug 29, 2017 at 20:04

Compared to the other answers, I feel like I'm taking crazy pills, because:

Is my following calculation correct?

Sorry to be the bearer of bad news, but no, this is not correct.

In 3 years, if the market gets soft, and I have to sell the house for \$200,000. Am I still better off than renting, because, \$180,000 (taking off 20k for the realtors and closing costs), less \$220,000 (\$40,000) is still smaller than 54k?

The math here is backwards. You have to add those two numbers together, not subtract! In the situation you described, after 3 years, you are out 54K+40K = \$94K if you buy, vs \$54K if you rent. (Because you pay the same \$54K for the mortgage, and then you lose another \$40K when you sell.) Then you get to subtract out whatever equity you've earned on the mortgage, which after 3 years will be somewhere in the \$12K-37K range depending on what your rate and term are. Even in the best case scenario (\$37K) you are still out 94-37 = \$57K if you buy. You also said the \$1500 was for your mortgage, but didn't mention taxes, insurances, and other fees. If those are not included in your mortgage payment then your starting number is going to be much higher than \$1500/month. If they are included, then the amount of equity you are going to get is going to be much less than \$37K. Note: you'll be able to deduct some of the interest and tax payments too, which will help lower the overall cost too.

If you are pretty sure you are going to be selling your home in as soon as 3 years, it's probably not going to make financial sense.

As a side note, a friend of mine recently sold his home that he owned for 12 years. He sold it for \$50K less than he paid, but had gained enough equity that after adding up all his costs for 12 years he estimated he came out ahead approximately \$100/month by owning vs renting an equivalent home. Note this also factored in the tax deduction advantage of owning a home. They key difference here is that he had 12 years to earn equity vs your scenario which is only 3 years.

• +1, and another cost of buying that is often overlooked is the opportunity cost of the down payment. If you pay 100k down on a house, a renter could put that into an index fund and make 2.5k/yr instead.
– Sam
Commented Aug 29, 2017 at 3:33
• @Sam Assuming rent stays the same and the fund makes more than one would pay for mortgage interest. Commented Aug 29, 2017 at 10:05
• +1 for actually answering the question.....and "crazy pills". Commented Aug 29, 2017 at 15:36
• @TTT, Thanks. I added a question with updated calculations here: money.stackexchange.com/questions/84408/…, could you confirm that the calculations are right? Commented Aug 29, 2017 at 17:43
• Take a dollar, throw out a banana.
– RLH
Commented Aug 30, 2017 at 20:54

There are other things you need to account for in your math:

• Property Taxes
• Home Insurance
• Utilities
• Maintenance
• Neighborhood dues (maybe)

Yes you build up equity in the house, but you still pay interest on your mortgage plus all of the above factors.

Closing costs of getting a mortgage should also be considered, but that's a one-time upfront cost and should be spread over the time that you own the home (you could also estimate the costs of selling the home in 5 years to be completely precise).

Mathematically if all of the above costs plus mortgage interest are less than your rent payment, then you'd be better off buying. You could also include the potential appreciation in home value, but that's not guaranteed by any means. I would argue that the appreciation would be roughly equal to future rent increases, so that could be a wash.

• Yes, when I said the same as rent for mortgage, that includes insurance, taxes, and neighborhood dues (which is none because this is a single family). Maintainance and Utilities on me. I pay for all utilities currently renting as well. Commented Aug 28, 2017 at 15:21
• @DStanley Loss of investment income on the down payment funds is a another factor to consider. Commented Aug 28, 2017 at 19:07
• Since you can sell the house once you've paid it off, wouldn't you be better off even if you mortgage+expenses are more than the costs of renting? Commented Aug 28, 2017 at 20:59
• If the interest + expenses are more than your rent, then no - you'd be better off renting. Commented Aug 28, 2017 at 21:03
• @Timbo - yes - but remember that any benefit from the mortgage interest deduction doesn't kick in until you make up the loss of the standard deduction. My realtor kept saying things like, 'But really, you're getting 25% off in taxes' but my only deduction was my mortgage interest and it was LESS than my standard deduction. So I actually saved nothing. Commented Aug 29, 2017 at 1:01

Am I better off?

Not necessarily.

Renting: Buying a service. You are paying 54k for the 'service' of housing. You do not own any asset.

Buying: Buying an asset, of course. Not only are you purchasing an asset, but you must also service the debt associated with it. You must also maintain the asset. This must all be done to provide yourself the same housing 'service' as renting.

1. You lost \$40k on the asset.
2. You serviced the asset for 3 years (taxes, maintenance, repairs, fees, utilities)
3. You also serviced the debt interest for 3 years (approx \$20k)

Without even estimating #2, it is clear you may not come out ahead in 3 years.

In addition, by holding mortgage debt you are now increasing your risk of exponentially more loss through foreclosure.

Owning a house is a long-term investment and can easily be more expensive than renting in the short term.

• 4. You have earned a tax benefit for 3 years. (perhaps \$15k) Commented Aug 29, 2017 at 16:35
• @VadimPonomarenko Yes, you have, but \$15k seems high. In the 25% tax bracket, writing off the debt interest of \$20k will save you about \$5k. Not seeing how you get close to \$15k here.
– jkuz
Commented Aug 29, 2017 at 16:44
• I used \$50k as debt interest. Looking again, this was high; however \$20k is low. I also used 30% tax rate as an estimate, which may include state and local taxes. My point is that you can't just compare (1)+(3) to \$54k, it's more complicated than that. Commented Aug 29, 2017 at 19:49
• @VadimPonomarenko gotcha. Makes sense, but I don't think it changes the answer. Thanks
– jkuz
Commented Aug 29, 2017 at 19:56

I actually did a very similar calculation recently, and I think it is a good exercise. It is difficult to be precise, but useful to get a general idea to help with your decision. Here is the general formula I used, which you will need to do once for buying and once for renting:

gross cost - value gained/saved = net cost

Deciding what goes into those categories is the crux of the problem. Here are some ideas:

• house payment
• home insurance
• lawn/yard care
• HOA fees
• utilities
• upkeep
• property taxes
• closing costs

Renting gross cost:

• Monthly rent
• non-included utilities
• renter's insurance
• parking fees
• non-refundable deposits

• equity gained (This was a little difficult to calculate as it depends on a lot of factors within a specific mortgage agreement and changes the longer you are paying. I assumed 15 yr fixed rate at 3.5% apr.)

Renting value:

• whatever reasonable value you can derive from lower rent like interest saved by paying off debts, or earnings from other investments. This is assuming that gross rent costs are lower than buying.

Obviously there are other incalculable things to consider (e.g. dealing with a landlord), but I think this calculated approach is helpful. For me, I roughly calculated that for buying a \$200k house approximately matched the value of paying \$900/month on rent (with 2 years in mind), so if that is the range you are in, if you can find a rental that matches your needs at around that cost or lower, then you are probably making a reasonable choice.

You need to look at the amortization calendar because after 3 years you'd might still owe greater than \$200,000 on the home. Depending on your down payment if you had put one down.

But let's say you put in 5% which is roughly \$11,000 you also have initial closing costs which might be another 3%

If the cost of your home went down that's all lost. Plus you'd have to cover what you still owed to the bank, making just the minimum payment draws down on the balance extremely slowly.

Owning the home also comes with costs you normally don't associate with renting, home insurance is higher than renters insurance. Property taxes are paid semi annually which don't come back to you either. There are many liabilities to take into account.

Ideally you'd want to sell when the home appreciates in value, by being a renter you don't get to partake in the housing market gains but you also don't risk anything during a downturn in the market. I've been on both sides of the equation as a renter and a buyer.

Sometimes the non monetary value is more important than the monetary ones, by being a renter I'm able to live in a nicer neighborhood because the home prices to purchase were too high. And as an owner there are always worries about maintenance items breaking down. As an owner I'm able to ride up this current market growth though, but there's essentially no gains if I sell my home if I bought back in because I'd be buying back into a higher priced market. Only way to really pull profits would be to sell my home and move to another state. (I'm in California)

The simple answer is no. After only 3 years in the property if it loses 20% of its value you won't be better off. Odds are you won't be financially ahead after only 3 years even if the property maintains its value.

As many others have pointed out, while renting many responsibilities fall on your land lord. When you buy, those responsibilities fall on you. There are many pitfalls to buying a house that most people do not know about that will increase the initial debt taken on when first buying. Private mortgage insurance (PMI), if you do not put enough money down or have a specific mortgage structure that doesn't require it. Closing costs, often rolled into the mortgage loan, increasing the amount owed and the interest paid. And, as HarrisonT pointed out, the amortization structure versus simple interest (ie car loan) that most people envision when borrowing money.

Regardless of what these additional responsibilities sum up to, you will not be ahead after only 3 years. The equity you build in 3 years is negligible. Mortgages are "front loaded", the bank totals all the interest they WOULD earn on your mortgage if you paid exactly your scheduled payment for the duration. Then they "amortize" it, the process by which they build an amortization table that says they will be collecting their interest first, and paying down the principle second.

The way you pay less interest and get ahead on a mortgage is to make additional principle payments. You have to be careful here too, because some banks/mortgage companies require you state you want to make additional principle payments explicitly, or they just apply your over payment to your next scheduled payment.

That's roughly correct, but rent includes things that won't be included when you own a home. Insurance, property tax, maintenance, maybe some utilities.

The actual calculation will be similar, but don't forget to add in all those other expenses to get a proper comparison between the two.

Having a mortgage tips many people over the threshold for itemizing deductions on their tax returns, so that can help offset some cost of ownership, but at the price you're looking at and the current low interest rates, it might not be that significant.

Youre missing the gross vs net. That is using the stove youre landlord thinks you should use is gross, and you will need a net to capture all of the bugs the old tenents allowed to fester in the property.

There is also the very real probability that your landlord will overcharge you for everything on moveout and make you replace a carpet that doesnt need to be replaced. Thats happened to me twice.

So add to the cost of renting the cost of having terrible appliances and things that cant be improved as well as your deposit.