Amortization Schedules and Principal Prepayment, Part 1: Shortening a 30-Year Mortgage Into 15

I’ve been tinkering around with my mortgage. Have you ever wondered how the monthly payment was determined? It’s called amortization. An amortization schedule is a way to make equal payments over a period of time, but have the payments split between principal and interest so that the interest paid over time decreases over time along with the loan amount remaining. It is a balancing act to be fair to both borrower and lender, and you can find a mathematical derivation here.

The most direct way to see where you are on your amortization schedule is to ask your lender to send you a copy. Alternatively, you can generate one yourself by using a mortgage calculator with this feature. Here is the amortization schedule for a $200,000 loan with a fixed interest rate of 5% over 30 years.

(May not be visible in RSS format. Here is the direct link.)

As you can see, in the beginning most of your payment goes towards interest, and only a little reduces your principal, or outstanding loan amount. As time goes on, your payment stays the same, but the chunk going towards interest decreases as the principal shrinks.

Mortgage Principal Prepayment
If you want to pay off the loan in less than 30 years, you’ll have to pay more than required. This is known as principal pre-payment. The effect of making such additional payments can be visualized by imagining that it moves you “ahead” in the amortizaton schedule.

Here’s an example using the schedule shown above. Let’s say you’re just getting ready to make your first payment of $1,074. At this rate, you still have 359 out of 360 monthly payments left to go! How much money would it take to shave off one extra payment off the end? To find that, you just have to look at the principal portion of Month #2, which I highlighted orange: $241.

If you pay $241 additional with your first payment now, you’ll won’t have to pay the $1,074 due on Month #360. Why is this? Working backwards, you can confirm that this is pretty much a 5% compounded return on $241 for 30 years, as expected. In addition, you’ll be shifted forward to Month #3 on the schedule. So next month your (still required) payment of $1,074 will have a bit more applied towards principal, and a bit less towards interest.

Making a 30-year Mortgage into a 15-year Mortgage
This actually creates an interesting way to shorten your mortgage. What if you kept paying the next month’s principal payment on top of your required $1,074 each month. You’d add on $241, then $243, then $245, and so on. Every month you’d shave off one month off the end, leaving you with a 15-year mortgage! You can also imagine this as skipping every other payment by just paying the principal and saving the interest.

This can work out nicely because the extra required will start out reasonably low at $241, and increase gradually with time along with your income and/or cashflow.

An alternative is to add $510 to every payment each month to shorten the term to 15 years. Although if you’re sure you want to do that, you might want to just get a 15-year fixed mortgage at a lower interest rate.

Read on in Part 2: Return on Investment Verification.

Comments

  1. Billy S. says:

    Your idea to pay the additional principle of the next payment is a wonderful idea for those who have reasonable expectations for salary increases! For example, teachers are paid based on experience and educational attainment. A new teacher who will be working toward a Master’s Degree or higher would eventually have the extra money to pay the $600-$700 a month extra that would be required towards the end of the 15 year period.

    I would however caution against the 15-year fixed mortgage. Having the option of the lower payment in the 30-year fixed is cheap insurance in case of emergencies (layoff, unexpected child, etc). One wouldn’t want to risk losing their home because they tried to pay it off too quickly.

  2. Or if you want a 5% return on your money, just pay it off. I spent a lot of time thinking about this issue and decided that being in the 28% tax bracket, it was not worth the deduction as opposed to how much I was spending in interest. I still have a mortgage but I only have to pay for a couple of years and 90% of my payments are going in my pocket rather then the banks. I could pay the remaining off but I am using that liquidity as some dry powder for the market woes. Another bonus is that with the Obama stimulas plans that people that either have no interest or not enough to offset the standard deduction they will still be able to deduct their real estate tax’s.

  3. Technically, that Wikipedia link is not a derivation. It’s an example with a formula. A derivation would be a proof where you derived the formula from principles.

    I sort of regularly run this kind of analysis against possible early retirement dates. My absolute earliest retirement date is in 2024, but my mortgage goes until 2035. If I add $120/month, my mortgage would expire in mid 2029, which might make a nice early retirement date.

  4. Wow. That was an extremely simple, straight-forward explanation of how to save tons of money on your mortgage.

    As a first-time homebuyer, this is something I’d love to try once we move.

    Great work!

  5. My lender actually has a calculator that lets be plug in different numbers for “extra monthly principle payment” or “one time payment”. It shows how many fewer payments I’d make over the life of the loan and the difference in interest paid over the life of the loan also. And of course if I plug in 0 for additional payments I get the regulator schedule.

  6. should you count on that much extra income down the road? It seems like if you are planning for the worst, you should pay more now and gradually lessen the amount, so if you lost an income source, you’d be further ahead of the game. I guess you could continue to make the extra payments from emergency savings…but I guess your priorities might change then too.

  7. Hrm, ya know I never thought abt how mortgages work.

    That formula is kind of interesting… now if only i rmbr’d enough to figure out how to derive it =)

  8. I’ve seen this idea before, and some plans go as far as making multiple principal payments in advance. For less drastic reductions which may be more palatable to some, as mentioned you could send an additional fixed amount each month (figure out what’s reasonable), send one extra full payment per year (which could reduce time on a 30 yr mortgage 6-7 yrs if you are consistent), or go biweekly.

    The last option comes at a cost as most “savings plans” are administered by a third party for an initial sign up fee. They don’t just hand over the money either. The net result of sending through a plan is very similar to sending a single extra payment on your own per year, just broken up a different way. Still, it will shave time off the mortgage.

    I’m interested in trying the amortization method and am hoping I can calculate it using the link(s) posted.

  9. Teeej,

    Using the rule of 72, and assuming 4% inflation, everything will double in price in approximately 18 years. (Your coffee, jeans, house value, salary etc.)

    So a $240 payment now actually has the same purchasing power as a $480 payment in month 216.

    Jonathan’s payment at that time would be $518, not $480, so really, it isn’t that much more than just the standard inflation adjustment. While the amounts seem larger, those amounts are 30 years from now. Just ask an older person what they paid for a house 30 years ago to get a first hand account of inflation!

    I personally don’t make extra payments as I prefer my money accessible. I think over 30 years, the stock market will do better than 5%. So I borrow at 5% and hopefully make more by investing than paying off my house. It’s the cheapest money you can borrow.

    An alternative way to think about this is… Has there been a 30 year period where a diversified portfolio did worse than 5%?

  10. JimmyDaGeek says:

    In case anyone wants to get a headache by deriving the formula, you are solving an algebraic equation where each month’s payment is equal to last month’s payment, AND, where each month’s payment consists of the interest on last month’s principal plus enough principal to make up the payment. This is why your interest payment goes down each month while your principal payment goes up.

    This is all tied up with present value and future value calculations.

  11. NoMoreWork says:

    Let me first say that I don’t own a home. However, I’ve played with the numbers before and think this is an excellent idea. The one benefit you didn’t mention is that if you get the 30yr instead of the 15yr and make the extra principle payments your REQUIRED monthly payment is a lot less. Thus, if you ever fall on hard times it is easy to back off the extra amount for period of time and not go into default. The 30yr + extra provides a nice safety cushion that doesn’t end up costing to much compared to a straight 15yr loan at lower interest.

  12. Yes, I also value the flexibility of a 30-year mortgage. The “minimum payment” is much lower vs a 15-year, and I can keep X months of it in reserve for tight times.

    Don – Yes, I kind of just meant how the number was derived. Here is a true derivation of the formula. I’m not geeky enough to try it myself (anymore).

  13. thanks for the post!

  14. Or cheap-os like me can do this with a 15-year mortgage and get it paid off in 7.5 years, with the 15 year payment being the fall-back in tighter times.

  15. Believe it or not, there are pros and cons to this. Understand that your 5% interest is only slightly higher than the rate of inflation. That means your money is also devaluing at slightly slower rate than it being paid off.

    That extra $240 you are spending now will likely have similar purchasing power to $1073 30 years from now. Probably slightly less, but if inflation goes up, than it will actually be worth more! However, 16 years from now, your salary will likely have increased at a much higher rate than the difference between inflation and your interest rate.

    In other words, by not making extra payments to your principal you can *often* maximize your total purchasing power throughout the 30 years. It’s an investment either way. It depends upon the rate of inflation. If inflation goes up drastically the $1073 will be a piece of cake to pay whereas you are spending the $240 of more powerful money that you could have used to actually obtain other goods.

    The constantly changing value of money (and houses for that matter) makes these sort of calculations a little more complicated.

    Some food for thought.

    For myself the extra money now is far, far more valuable than paying off the mortgage in the future. But everybody’s situation is different.

  16. auntie_green says:

    I think this is a good idea as long as its not in lieu of other “savings” – ie , if you can still max out your 401(K) and then pay extra to the mortgage, do it. But I wouldn’t pay extra to the mortgage in lieu of maxing out the 401(k) and putting cash away for a rainy day

  17. i just refinanced down from 30 (had 25 left) to 20 and cut my monthly payment by $60.
    i made sure i got the amortization table from the bank so i can look at pre-pay options, which I plan to use and track carefully.

    my father-in-law still has the amortization table from when he bought his home in the early 80′s. he has marks by all his payments and pre-payments. he is long since paid off, but he has kept the page of a reminder of the times and all the work it took to get there.

  18. Maybe I should look at the formula, but I don’t really see how paying almost nothing but interest in the beginning is “fair to the borrower.”

  19. Most people tend to freak out when they see that over the course of 30 years, the amount of money going toward interest is almost as much as the cost of the home itself (in your case $186,640 goes towards interest over 30 years). But if you can earn more on your money than the 5% (who knows the answer to that really?), then you’re better off keeping the mortgage.

  20. auntie_green says:

    Jules’ comment might be worth a whole post on its own. “Fair to the borrower” has been getting a ton of press today, with Obama coming out on credit cards (I know, credit cards are different than mortgages, but “fair to borrower” remains the same in both instances)

    I know I’m going to get a LOT of negatives here. But “fair to borrower” irks me. If as a borrower, you don’t like the terms being offered, don’t borrow!

  21. @Auntie: I get what you’re saying about just not borrowing, and agree in principle, but if all the companies have the same terms, what choice does a consumer have?
    If I want a house without a loan, it would take me 30 years to save up enough for it! At that rate, I might as well just take out a loan, even with not so great terms.

  22. Jules/Auntie/Sarah – amortization is just math. Because a larger balance means more interest, it works out that the first payments are almost all interest. That interest due on the first payment is whatever it is given the balance and the rate (balance*interest rate/12=X). So the only way for the first payment to have more effect on principal would be to pay more, which you can do by shorting the period (maybe to a 15 year loan, even more on a 10 year loan, etc.) or pay higher payments at first which would effectively shorten the length of the loan (extra principal payment), both of which are an option someone can take. Sure you could just call some of the interest payment principal payment if that makes you feel better, but all the interest is then not getting paid and would have to be re-capitalized and you’d end up in the same place.

    Lets leave the “fair to borrower” language to issues it could logically apply to, like mortage companies upping the rate on you the day of the closing after you’ve placed a deposit, crooked appraisals, etc. Math is not out to get you.

  23. JimmyDaGeek says:

    @Jules/Auntie/Sarah
    I want to add to what Strick wrote. Do you believe it is “fair to borrower” to pay all the interest on the money borrowed? If so, how often?

    Contrary to popular delusions, mortgages are not “front-loaded”, regardless that you pay mostly interest in the beginning. When you pay back a typical loan for a house, car, etc. you are paying interest on the balance owed for the entire previous month. I believe that mortgages calculated this interest by dividing the interest rate by 12 and multiplying it against the current balance, regardless of the number of days in the month. If you look at your amortization table and make the interest calculation, you will see that your monthly payment also includes enough principal to make your total payment the same as the last month. There is nothing keeping you from paying more principal, if you want to make things “fairer”

  24. @Sarah: if you want to use an extreme example, the other choice a consumer has is to not buy something you can’t afford – i.e. don’t borrow. It wouldn’t take 30 years to save the entire amount because you’re not going to spend all that extra money on interest. In fact it would probably take significantly less if you use compounding interest in your favor instead of the banks! You’re not the victim here – you just want to own a house before you can afford it, plain and simple. That being said, I’m not anti-mortgage, but I’m not going to complain about one either.

    On a different note… for those who make the but-I-can-make-more-than-5% argument, that’s generally true but I did want to throw in the idea that debt = risk, and there’s a hard-to-define element that you can ride out a pretty hard time with minimal payments assuming your house is paid off. I think investing before paying off your home is smart, but you have to be aware that you’re taking a risk vs. a level of stability/certainty.

  25. Plenty of people say they will take out a 30 year mortgage and be disciplined enough to pay it off early or invest the difference but only a very small percentage actually do it. Those who say they can make a better return by investing in stock market should consider actual investor behavior, since the average investor only earned a market return of 4.5% between 1987 and 2007 while the S&P 500 Index averaged 11.8% according to a Dalbar Inc study. If your priority is to have a paid off mortgage by a certain date, then you should get a mortgage that coincides with that goal whether it is 25, 15 or 10 years. This will force you to be disciplined by paying more toward your mortgage each month as well as increasing your emergency fund to meet the payments in the event that you can no longer make them for a period of time.

  26. Strick, math is out to get me…my jr. high and high school math grades prove it. ;-)

    Okay, seriously though, I do have a recently diagnosed learning disability in math, so maybe I just don’t get it. But, doesn’t it really only work out to be “fair” if the borrower stays in the house all 30 years? Granted, I don’t know what the solution would be to make it more fair when it’s impossible to know how long someone will stay in their house.

    Auntie Green, sorry I “irked” you. But really, I don’t have $200k in cash laying around, so borrowing for a mortgage was my only option…well, besides a yurt. And Jimmie DaGeek, my paycheck would be what is preventing me from making more payments on the principal.

  27. Bummer that I suggested this in earlier post comments regarding paying down principal and in email to author and didn’t even get a shout out…

  28. so my mortgage is for 219 K at 5.0 fixed (bought in march 08). and the county says my house is now only worth 149k. and my time horizon for moving is less than 7 years…. i should still “get divorced, go bankrupt, and get forclosed on” while my “ex wife” uses the “settlement money” to purchase a new house, at which point we “reconcile our differences and give the marriage another shot”… right? i mean that seems to be the only rational thing i can do here…

  29. What if I’m planning on selling the house in 3 to 4 years? Is is still worth doing?

  30. JimmyDaGeek says:

    @Jules

    If you don’t have enough cash to prepay your mortgage on your own, how do you expect MMA to do it for you?

  31. Can someone who has actually run the numbers answer the following question:

    When comparing a 30 year mortgage to a 15 year mortgage with equal interest rates, would you end up paying the same amount of interest if the 30 year loan is paid off in 15?

    Seems like a straightforward question, but when do the payments in a standard 30 year loan reach an equilibrium between the interest and the principle? If it is after the 15th year, wouldn’t that mean that the front half of the loan contains more interest; thus resulting in a greater amount of interest being paid over those first 15 years of the 30 than during the life of the actual 15 year loan? (sorry for being so wordy, just trying to be specific)

    Thanks for your help

  32. JimmyDaGeek says:

    @T-W

    With respect to paying off a 30 yr loan in 15 yrs. If you make the same monthly payment that you would have for a 15 year loan, then the loan will perform exactly like a 15 year loan because you will pay off the principle at the same rate. You will pay the same amount of interest.

    To answer your second question, here is a link where you can play to your heart’s delight: http://dinkytown.com/java/MortgageLoan.html

  33. Actually, T-W, it all depends on your interest rate. If your 15-year and 30-year had the same interest rate, paying off the 30-year in 15-year would cost the same in total payments.

    However, in most cases the 30-year has a higher interest rate so if you were to make the same monthly payments as the 15-year mortgage, it would take longer than 15 years to pay off the 30-year mortgage. It might take something like 16 years.

    More details here.

  34. Christine says:

    man, this is a great post. didn’t get around to reading it til just now, but i love the way you explained it. i’ll definately be doing this once i purchase my first home. thanks Jonathan~

  35. I’m late to this discussion too, but reading about the “fair to the borrower”, that’s not really the goal of amortization, it’s to provide equal payments to allow the borrower to budget.

    The alternative would be to pay the monthly interest, plus a fixed principal payment. To keep the numbers a little simple, use $120K at 5% for 20 years. Amortization gives fixed TOTAL payment of $795 every month for 20 years. The alternative would give fixed PRINCIPAL payment of $500 ($120K divided by 240 months).

    Now it looks “fair”. But instead of $795 the first month you are paying $1,000. The next month $997.92 and it keeps getting smaller each month, but after 10 years you’re still at about $750/month.

    You might consider this “fair” to the borrower but probably a lot harder to afford.

  36. I have a $200k mortgage and $100k cash. Shall I use $100k cash to pay the principal, or shall I keep the cash in the bank or other investments?

  37. JimmyDaGeek says:

    @Aria
    It depends ;)

    Are you secure in your job? What are your thoughts about the economy for the next 20 years or so? You didn’t tell us how long your mortgage is now.

    People who pay down their mortgage quickly like the idea of being debt-free. Some people are unsure about our economics and would prefer to go with a sure thing of paying off debt. There is no sure thing in investing. If I had that chunk, I would be looking at good dividend-paying stocks to help pay the interest. Hopefully, it would be wash, tax-wise, with the dividend income offset by the mortgage interest. I believe that dividend income get special tax treatment right now, so you might come out slightly ahead.

  38. Thank you JimmyDaGeek for your comment. My mortgage actually consists of 2 loans – $150k @ 6.5% and $50k @ 3% (silent loan). I’m at payment 26 of my 30 year loan. I work for the city government, and so far I think my job is secure. I cannot refinance if I don’t pay off the 2nd silent loan. My thinking is to pay down the principal to my 1st loan, so I don’t pay so much interest. But my friend suggests me pay off the 2nd loan and do the re-finance. However, the 2nd loan’s interest rate is 3% and it’s a silent loan (I don’t need to pay till the 1st loan is all paid off). I wonder whether I should pay down the principal of my 1st loan, or to pay off the 2nd loan & do the re-finance. Which one saves me more money (interest & tax wise)? I can’t seem to figure it out mathematically. Help! Thanks a lot.

  39. what I dont understand is why dont they just allow us to pay ALL principal first and then make payments for the interest based on how long it took us to pay off principal or they could add $10,000 or a flat rate onto our mortgage. I would much rather pay $10000 than $175,000 for a $79,000 condo that I would rather not be paying on for the rest of my life. But as we all know the banks run this country and will not likely change. In the meantime I will probably change to a 15 year mortgage.

  40. @Aria
    You calculate the combine interest of two loans. You will know if refinance will save you money. Base on the number you provided, 150k @6.5% and 50k @3%, the combine interest in about 5.4%.

    So, if you refinance with a better rate than 5.4%, which you can with the current market, you will come out ahead.

    Hope it helps.

  41. I was told that it is possible to pay off the principal at the end of the loan, #360 for a 30 year, to eliminate that interest. It is much cheaper, but as your income grows, and you pay from the “end of the mortgage on principal”, it’s the same, but cheaper and will eventually end up in the middle at 15 years. True??

  42. market_works says:

    Would you reasonably expect to make more than 5 percent returns in the stock market. Most who do a little bit of homework and investing on their own comfortably make more than 10 percent with small sums in the market.
    Not a good idea to pre-pay.

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