What equity would I have when selling early on in mortgage?

Question

I'm trying to wrap my head around the idea of mortgages, and I hope someone can help me.

Say I buy a house for $100,000. I put down $20,000, and get an $80,000 mortgage. I've heard that for the first few years, I'll only be paying down the interest of the mortgage, and not the principal (for argument's sake let's say it takes 5 years to start paying off principal).

But, 4 years into the mortgage I decide to sell this house. At this point, I'm still only paying interest. Other than the down payment, do I have any equity in the house? If it sells for $100,000 again, what would be my share?

Answer 1

I've heard that for the first few years, I'll only be paying down the interest of the mortgage, and not the principal

Interest-only mortgages might be available to you, but otherwise that's not correct.

For a repayment mortgage, the lender calculates (on the counter-factual assumption that the interest rate will not change through the life of the mortgage) how much you need to pay each month to ensure that the principal will be paid down to zero after the agreed amortization period. So in the first month the principal is $80k, the interest is some fraction of that, I will call it X. You pay your monthly payment, Y, and Y-X is deducted from the principal.

In the second month the interest is a fraction not of $80k, but of $80k + X - Y. So in the second month the interest is slightly less than X, but your monthly payment is still Y. Thus in the second month the principal is reduced by slightly more than Y-X, and so on. Eventually in the final month of the mortgage you pay off 100% of the remaining principal.

An interest-only mortgage is simply one for which (by agreement with the lender) Y = X. That is, the monthly payments do not pay down the principal, ever. At the end of the mortgage you have to find the full amount loaned, because you still owe the bank the full amount.

If you end a repayment mortgage early then the lender uses this system of regular monthly interest charges and regular monthly payments to calculate your remaining principal. Then they'll add any administration charges or early repayment penalties on top of that calculated principal.

Whenever the interest rate changes (or the mortgage otherwise changes) your monthly payment is re-calculated to still hit your target repayment date, and the bank tells you your new payment.

As an issue of mathematics and in particular the effects of compound interest, it turns out that if the mortgage is amortized over a long period, you don't pay off much in the first 5 years. You do pay off something, but it's small enough that people will say, as an approximation, that in the early years you "don't pay off the principal". soakley shows some example figures, it depends on the interest rate and the repayment period.

So, if it were really true that you only pay off interest in the first 5 years (for example if the mortgage you choose to take is an interest-only mortgage), then at the end of 5 years your equity in the house would be the value of the house less the $80k that you still owe to the bank. Looking at it another way, your equity is your $20k up-front payment plus all of any increase in the value of the house (or minus all of any decrease, as the case may be). Assuming no change in the value of your house: $100k asset minus $80k debt equals $20k equity.

However if you have a repayment mortgage then you will in fact pay off a small amount in the first 5 years and so your equity will be more than $20k assuming no change in the value of the house.

Note also that there's no question of "shares" in the value of the house. People talk about the bank owning 80% of their house but that's not true (except in less common arrangements such as Islamic mortgages). You will own 100% of the house and owe the bank $80k (less whatever you've paid down). That's why all of the increase or decrease in the value of the house is yours.

Answer 2

Four years into the mortgage, here is a table showing how much principal you would be able to pay off assuming a 30-year amortization with a fixed interest rate and a monthly payment.

Rate        Paid Off
3%          6992
4%          5989
5%          5096
6%          4308

The amount of interest that is paid each month can be easily calculated by multiplying the interest rate (adjusted to the monthly level) by the remaining principal.

So, for example, at 6%, the first payment will include (0.06/12)*80000 = $400 in interest. The total payment can be calculated with spreadsheet software to be $479.64, so you would be paying off $79.64 on the principal with the first payment.

Answer 3

Equity is made up of the amount of any principal you pay off plus any capital gain - costs on the investment.

Unless you have an interest only loan you will pay off part of the principal from the start, however it will be a very small part at first and will increase as time passes and you pay more and more of the principal off.

If you sell for the same price as you bought at after 4 years it may be likely that you have less than your initial $20k, as the costs of buying and selling would probably be more than any equity you have made up in paying off part of the principal.

Answer 4

You are getting a $80,000 mortgage. Note that many mortgage lenders will try to convince you to get a higher mortgage so that you can pay for needed repairs to the house (or go on holiday, buy a car, or waste the money in many ways). The prudent thing is to get the $80,000 mortgage and make any repairs and improvements to the house as you can afford them, so you live in a nicer house and a house that might become worth more than $100,000.

On the mortgage, you pay interest for the amount that you currently owe ($80,000) and the rest of your payment pays of the principal (the amount that you owe). I calculated that to pay back $80,000 over 30 years at 6% per year (0.5% per month), you'd have to pay about $480 a month. In the first month, $400 of your $480 is interest payment, only $80 of the $80,000 is back. In the second month, you owe $80 less. You pay 0.5% of $80 less interest, that's 40 cents. So in the second month you pay back $80.40. In 30 years time, almost all the $480 you pay comes off the principal.

So saying "at the beginning of the mortgage, you only pay interest" is exaggerated, but not that much. In the first month, only $80 of $480 are repayment. In ten years time, $145 will be repayment. In 20 years time, $264 is repayment. The effect is stronger the longer your mortgage and the higher the interest. At 12% interest over 30 years, you'd pay $822.89 a month, of which $800 is interest. Paying back $900 a month would mean you are paid back in 18 1/2 years instead of 30 years.

My calculation is that at 6% over 30 years, after four years you would owe $75,670 instead of $80,000. So if you sold for $100,000 again, you'd have $100,000 - $75,670 = $24,330. There are probably fees etc. and my calculation and the bank's calculation are not the same, but you will have some additional money, just not very much.

Answer 5

This is in regards to your latest comment prompt, and not necessarily the question.

You said:

Ooh, that's a bummer, but a good thing to be aware of. So in the above situation, I guess it would have been better to rent for the 4 years.

Ben Jackson's original statement doesn't take into consideration your payments toward your principal(which others have covered sufficiently). I'd recommend you look at your monthly statement or talk to your loan provider to figure out how much you've payed so far(rather than looking at tables online, which might not be 100% accurate anyways).

Concrete example:

Let's say you find out that you've paid $X towards your principal so far. That means, out of your total $100,000, you've paid $20,000 + $X. If you sell your house at $100,000, you'll end up having $20,000 + $X in your pocket, minus any fees from realtors, closing, etc(the fees Ben Jackson mentioned). This is low-balled for round numbers, but for example, say you have paid $4,000 into your principle and your fees total $8,000, you'll end up with $16,000 in your pocket after the 4 years. Of course, you started out with $20,000 so now you actually have less. The breakeven point is where principle payments = selling fees, and there's no way we can calculate that for you, you just have to look it up yourself. Even this, in itself, is a bit rudimentary. From my experience with a $120,000 house, my fees were far less than $8,000 at around $3,000-$4,000(don't remember precisely anymore), and my principle payments had reached the $4,000 mark long before the 4 year mark. All in all, it's just totally dependent on variables only you know(assuming this is a house you currently own and are looking to sell).

Things that may help your situation:

• Increased value in home: if you sell for $120k, you've essentially *poofed* +$20k into your pocket. Conversely, if you sell for $80k you may be in a bit of trouble(the reason you made a down payment is to mitigate this kind of trouble, that down-payment is your buffer against having to owe anything in the event your home depreciates in value, but it doesn't always protect you).
• Paying more than the minimum towards your principle each month. If you can do this, I would suggest giving it a shot. Per Soakley's answer, your first month's payment to principle might only have been $80, with the rest going to interest. If you're able to drop in an extra $100 or $200, that's a massive improvement in paying down your principle, and if you're planning on staying for a long time that's the best way to cut costs on interest payments as well.

4 years is a short period to own a house, but you can certainly make it worth it if you plan correctly. If you don't own but are actually in the market and think you might only be around for 4 years, check the prices in your area. If they're low, with low interest rates, it might be highly beneficial. Housing markets can change a lot in 4 years, and you might end up in a good situation where you buy low and sell high(the investor's dream!).

Ultimately, you'll have to crunch some numbers to figure out whether renting or owning is better for you(or would have been better).