How do amortization schedules work and when are they used?
An amortization schedule is often used to produce identical payments for the term (repayment period) of a loan, resulting in the principal being paid off and the debt retired at the end of the loan. This is in contrast to an interest only, or balloon loan. These loans require little or no payment against the balance of the loan, requiring the loan to be paid indefinitely if there is no term, or requiring the loan to be entirely paid off from cash or a new loan at the end of the term. A basic amortization formula can be derived from the compound interest formula:   This formula comes from the Wikipedia article on amortization. The basics of the formula are the periodic payment amount, A (your monthly payment), can be determined by the principal loan, P, the rate, r, and the number of payments, n.  Lenders lend money to make a profit on the interest. They'd like to get back all the money they lent out. Amortization schedules are popular because the fixed low payments make it easier for borrowers to pay the loan off eventually. They also tend to be very profitable for lenders, especially at the start of the term, because they make a lot of profit on interest, just like the start of your mortgage. The principal of a mortgage has more meaning than the principal of a revolving debt credit card. The mortgage principal is fixed at the start, and represents the value of the collateral property that is your home. You could consider the amount of principal paid to be the percentage of your home that you actually own (as part of your net worth calculation).  A credit card has a new balance each month depending on how much you charge and how much you pay off. Principal has less meaning in this case, because there is no collateral to compare against, and the balance will change monthly. In this case, the meaning of the amortization schedule on your credit card is how long it will take you to pay off the balance if you stop charging and pay at the proscribed payment level over the term described. Given the high interest rate on credit cards, you may end up paying twice as much for goods in the long run if you follow your lenders schedule. Amortizing loans are common for consumer loans, unless a borrower is seeking out the lowest possible monthly payment. Lenders recognize that people will eventually die, and want to be paid off before that happens. Balloon and interest only bonds and loans are more commonly issued by businesses and governments who are (hopefully) investing in capital improvements that will pay off in the long run. Thousands of people and businesses have gone bankrupt in this financial crisis because their interest only loans reached term, and no one was willing to lend them money anymore to replace their existing loan. Amortization is the process by which your loan balance decreases over time. For both mortgages and credit card balances, your interest charges are based on what you owe.  The calculation of the balance is a little different, but it still is based on what you owe. You're observing correctly that most of the first payments on a mortgage are interest.  This stands to reason since an amortization schedule (for a fixed-rate mortgage) is constructed on the assumption that you're making your payments equally over the course of the mortgage.  Since you owe more at the beginning, you accrue more interest, and a larger fraction of your payment is interest.  Near the end, you owe little, and most of your payment, therefore, is principal. Both Credit Card and Mortgage work on same principle. The interest is calculated on the remaining balance.  As the balance reduces the interest reduces. The Mortgage schedule is calculated with the assumption that you would be paying a certain amount over a period of years. However if you pay more, then the balance becomes less, and hence the subsequent interest also reduces. This means you would pay the loan faster and also pay less then originaly forecasted. The other type of loan, typically personal loans / auto loans in older days worked on fixed schedule. This means that you need to pay principal + Pre Determined interest. This is then broken into equal monthly installment. However in such a schedule, even if you pay a lumpsum amount in between, the total amount you need to pay remains same. Only the tenor reduces. Simply put, for a mortgage, interest is charged only on the balance as well. Think of it this way - on a $100K 6% loan, on day one, 1/2% is $500, and the payment is just under $600, so barely $100 goes to principal. But the last payment of $600 is nearly all principal.  By the way, you are welcome to make extra principal payments along with the payment due each month. An extra $244 in this example, paid each and every month, will drop the term to just 15 years. Think about that, 40% higher payment, all attacking the principal, and you cut the term by 1/2 the time.
How does compounding of annual interest work? answers this question. It's not simple compound interest. It's a time value of money calculation similar to mortgage calculations. Only the cash flow is the other way, a 'deposit' instead of 'payment'. When using a finance calculator such as the TI-BA35 (Note, it's no longer manufactured, but you can find secondhand. It was the first electronic device I ever loved. Seriously) you enter PV (present value) FV (future value) Int (the interest rate) nPer (number of periods) PMT (payment).  For a mortgage, there's a PV, but FV = $0. For you, it's reversed. PMT on this model is a positive number, for you it's negative, the amount you deposit. You also need to account for the fact that a mortgage is paid on day 31, but you start deposits on Day 1. See the other answer (I linked at start) for the equations. Many people, especially with lower income/skill/education, have poor money management skills to the point where they will not be able to ration their money for a full month. If the payment schedule is reduced to weekly or bi-weekly it becomes easier for such people to make non-discretionary payments. "There is no formula that can be applied to most variations of the problem you pose.  The reason is that there is no simple, fixed relationship between the two time periods involved: the time interval for successive payments, and the time period for successive interest compounding. Suppose you have daily compounding and you want to make weekly payments (A case that can be handled).  Say the quoted rate is  4.2% per year, compounded daily Then the rate per day is 4.2/365, or 0.0115068 % So, in one week, a debt would grow through seven compoundings.  A debt of $1 would grow to 1 * (1+.000225068)^7, or 1.000805754 So, the equivalent interest rate for weekly compounding is 0.0805754% Now you have weekly compounding, and weekly payments, so the standard annuity formulas apply. The problem lies in that number ""7"", the number of days in a week.  But if you were trying to handle daily / monthly, or weekly / quarterly, what value would you use? In such cases, the most practical method is to convert any compounding rate to a daily compounding rate, and use a spreadsheet to handle the irregularly spaced payments." "they apply it to my next payment That's what my bank did with my auto loan.  I got so far ahead that once I was able to skip a payment and use the money I would have sent the bank that month for something else.  Still, though, I kept on paying extra, and eventually it was paid off faster than ""normal"". EDIT:  what does your loan agreement say is supposed to happen to extra payments?" I think they're compounding the interest daily. That means you have to look at the number of days between payments to judge how much the interest charge is. From February 3 to March 2 is 28 days (2012 was a leap year). From March 2 to April 3 is 32 days. That's an increase of about 14% in number of days between payments, which accounts reasonably well to the ~$18 difference in interest charge.  Daily compounding also explains the minor fluctuations in the other interest charges. I think if you compute interest/day for each month, you'll find that it is, indeed, decreasing over time. In the prior PMI discussions here, it's been stated that the bank is not obligated to remove PMI until the mortgage's natural amortization puts the debt at 78% LTV. So, paying in advance like this will not automatically remove the PMI.  Nor will a lump sum payment be certain to move the next payment ahead a year. If it's entered as a principal prepayment, the next month's payment is still due. In the world of coupon books, if you sent in a year's payments, you'd not benefit from the interest saved, in one year you'd owe what the amortization table tells you.  There's no free lunch when it comes to mortgages or finance in general. This is why we usually caution that one should not be cash poor the day after buying a house. Best to save 30%, put down 20%, and have a cushion after the closing. "Here's an example that I'm trying to figure out.  ETF firm has an agreement with GS for blocks of IBM. They have agreed on daily VWAP + 1% for execution price.  Further, there is a commission schedule for 5 mils with GS.  Come month end, ETF firm has to do a monthly rebalance. As such must buy 100,000 shares at IBM which goes for about $100  The commission for the trade is 100,000 * 5 mils = $500 in commission for that trade. I assume all of this is covered in the expense ratio. Such that if VWAP for the day was 100, then each share got executed to the ETF at 101 (VWAP+ %1) + .0005 (5 mils per share) = for a resultant 101.0005 cost basis  The ETF then turns around and takes out (let's say) 1% as the expense ratio ($1.01005 per share)  I think everything so far is pretty straight forward. Let me know if I missed something to this point.  Now, this is what I'm trying to get my head around. ETF firm has a revenue sharing agreement as well as other ""relations"" with GS. One of which is 50% back on commissions as soft dollars. On top of that GS has a program where if you do a set amount of ""VWAP +"" trades you are eligible for their corporate well-being programs and other ""sponsorship"" of ETF's interests including helping to pay for marketing, rent, computers, etc.   Does that happen? Do these disclosures exist somewhere?" "I recently requested an off-schedule escrow analysis. We refinanced a house in August and the servicer got confused about when the home owner's insurance was due (in October). They refunded the ""insurance"" money to us in September. That combined with the fact that the insurance amount was different than what they expected, made me request the escrow analysis. That way I can decide whether to pay up the escrow account now or do it over the next year. The servicer agent just said that the monthly payment amounts might change again in January when they do the usual analysis. If you like to set up automatic payments, that would be a downside. I haven't done that yet, so not a problem for me." When I called Navient about this exact question last year they told me that my loan is a term length loan; so if I were to make extra payments on one of my dozen loans then my total monthly payment would be adjusted (go down) in order to make sure that my loans would still be paid off in x months.   It is very important to note however that Navient has at least 4 loan payment types that I know of so I can make no assurances that yours will work the same way.  The only way to get an absolute answer to this is going to be to Call Navient and ask them. "There are some loan types where your minimum payment may be less than the interest due in the current period; this is not true of credit cards in the US.  Separately, if you have a minimum payment amount due of less than the interest due in the period, the net interest amount would just become principal anyway so differentiating it isn't meaningful. With credit cards in the US, the general minimum calculation is 1% of the principal outstanding plus all interest accrued in the period plus any fees.  Any overpayment is applied to the principal outstanding, because this is a revolving line of credit and unpaid interest or fees appear as a charge just like your coffee and also begin to accrue interest.  The issue arises if you have multiple interest rates.  Maybe you did a balance transfer at a discounted interest rate; does that balance get credited before the balance carried at the standard rate?  You'll have to call your lender.  While there is a regulation in place requiring payment to credit the highest rate balance first the banks still have latitude on how the payment is literally applied; explained below.   When there IS an amortization schedule, the issue is not ""principal or interest"" the issue is principle, or the next payment on the amortization schedule.  If the monthly payment on your car loan is $200, but you send $250, the bank will use the additional $50 to credit the next payment due.  When you get your statement next month (it's usually monthly) it will indicate an amount due of $150.  When you've prepaid more than an entire payment, the next payment is just farther in to the future.  You need to talk to your lender about ""unscheduled"" principal payments because the process will vary by lender and by specific loan. Call your lender.  You are a customer, you have a contract, they will explain this stuff to you.  There is no harm that can possibly come from learning the nuances of your agreement with them. Regarding the nuance to the payment regulation: A federal credit card reform law enacted in May 2009 requires that credit card companies must apply your entire payment, minus the required minimum payment amount, to the highest interest rate balance on your card.  Some credit card issuers are aggressive here and apply the non-interest portion of the minimum payment to the lowest interest rate first.  You'll need to call your bank and ask them." Why won't anyone just answer the original question? The question was not about opportunity cost or flexibility or family expenses. There are no right answers to any of those things and they all depend on individual circumstances. I believe the answer to the question of whether paying off a 30-year mortgage in 15 years would cost the same amount as a 15-year mortgage of the same interest rate is yes but ONLY if you pay it off on the exact same schedule as your supposed 15-year. In reality, the answer is NO for two reasons: the amortization schedule; and the fact that the 30-year will always have a higher interest rate than the 15-year. The way mortgages are amortized, the interest is paid first, essentially. For most people the majority of the monthly payment is interest for the first half of the loan's life. This is good for most people because, in reality, most mortgages only last a couple years after which people refinance or move and for those first couple years the majority of one's housing costs (interest) are tax deductible. It is arguable whether perpetuating this for one's entire life is wise... but that's the reality of most mortgages. So, unless you pay off your 30-year on the exact same amortization schedule of your theoretical 15-year, you will pay more in interest. A common strategy people pursue is paying an extra monthly payment (or more) each year. By the time you get around to chipping away at your principal in that way, you will already have paid a lot more interest than you would have on a 15-year. And, really, if you can afford to substantially pay down principal in the first year or two of your mortgage, you probably should've borrowed less money to begin with. In theory, IF the rates were the same (they're not) and IF you paid the 30 off every month in the EXACT same way as you would've paid a 15 (you won't) you will pay the same amount in the end. You have to decide if the flexibility is worth more to you than the cost savings.  For example: a 300k mortgage at 3.5% will have a monthly payment of ~$2150 for a 15-year and ~$1350 for a 30-year, both will start with ~$875/month of that being in interest (gradually declining with time). What I think most people undervalue is the freedom and peace of mind that comes with a paid off or nearly paid off home... and 15 years is a lot more tangible than 30, plus a lot cheaper over all. If you can afford a 15-year mortgage without putting too much stress on your budget, it is definitely the better option for financial security.  And be careful of the index fund opportunity cost advice. On average it may be a good idea when you look at the very long run, historically, but a lot of people get less than average returns depending on when they buy and what the market does in the short run. There is no certainty around what returns you will get from the stock market, but if you have a 30-year mortgage there is a lot of certainty around what you will owe every month for the next 30-years. Different mixes of investments make sense for different people, and most people would be wise to get some exposure to the stock market for its returns and liquidity. However, if someone's goal is borrowing more money for their house in order to invest more money in the stock market for their retirement, they would actually be better served in achieving security and independence 15 years sooner. "a link to this article grabbed my Interest as I was browsing the site for something totally unrelated to finance.  Your question is not silly - I'm not a financial expert, but I've been in your situation several times with Carmax Auto Finance (CAF) in particular. A lot of people probably thought you don't understand how financing works - but your Car Loan set up is EXACTLY how CAF Financing works, which I've used several times. Just some background info to anyone else reading this - unlike most other Simple Interest Car Financing, with CAF, they calculate per-diem based on your principal balance, and recalculate it every time you make a payment, regardless of when your actual due date was.  But here's what makes CAF financing particularly fair - when you do make a payment, your per-diem since your last payment accrued X dollars, and that's your interest portion that is subtracted first from your payment (and obviously per-diem goes down faster the more you pay in a payment), and then EVerything else, including Any extra payments you make - goes to Principal. You do not have to specify that the extra payment(S) are principal only. If your payment amount per month is $500 and you give them 11 payments of $500 - the first $500 will have a small portion go to interest accrued since the last payment - depending on the per-diem that was recalculated, and then EVERYTHING ELSE goes to principal and STILL PUSHES YOUR NEXT DUE DATE (I prefer to break up extra payments as precisely the amount due per month, so that my intention is clear - pay the extra as a payment for the next month, and the one after that, etc, and keep pushing my next due date). That last point of pushing your next due date is the key  - not all car financing companies do that. A lot of them will let you pay to principal yes, but you're still due next month. With CAF, you can have your cake, and eat it too. I worked for them in College - I know their financing system in and out, and I've always financed with them for that very reason.  So, back to the question - should you keep the loan alive, albeit for a small amount. My unprofessional answer is yes! Car loans are very powerful in your credit report because they are installment accounts (same as Mortgages, and other accounts that you pay down to 0 and the loan is closed). Credit cards, are revolving accounts, and don't offer as much bang for your money - unless you are savvy in manipulating your card balances - take it up one month, take it down to 0 the next month, etc. I play those games a lot - but I always find mortgage and auto loans make the best impact.  I do exactly what you do myself - I pay off the car down to about $500 (I actually make several small payments each equal to the agreed upon Monthly payment because their system automatically treats that as a payment for the next month due, and the one after that, etc - on top of paying it all to principal as I mentioned).  DO NOT leave a dollar, as another reader mentioned - they have a ""good will"" threshold, I can't remember how much - probably $50, for which they will consider the account paid off, and close it out. So, if your concern is throwing away free money but you still want the account alive, your ""sweet spot"" where you can be sure the loan is not closed, is probably around $100.  BUT....something else important to consider if you decide to go with that strategy of keeping the account alive (which I recommend). In my case, CAF will adjust down your next payment due, if it's less than the principal left. SO, let's say your regular payment is $400 and you only leave a $100, your next payment due is $100 (and it will go up a few cents each month because of the small per-diem), and that is exactly what CAF will report to the credit bureaus as your monthly obligation - which sucks because now your awesome car payment history looks like you've only been paying $100 every month - so, leave something close to one month's payment (yes, the interest accrued will be higher - but I'm not a penny-pincher when the reward is worth it - if you left $400 for 1.5 years at 10% APR - that equates to about $50 interest for that entire time - well worth it in my books. Sorry for rambling a lot, I suck myself into these debates all the time :)" "Is there more on where Dalio gets his definitions for the short-term debt cycle (5-8 years or so) and ""deleveraging"" and the long-term debt cycle (75-100 years)? (or his evidence that separates the two)?  At one point 18:10, he says the difference is that in a deleveraging, interest rates hit 0 and can no longer go lower, but I don't know if that works as a definition per se.  There are other things that central banks do when interest rates hit 0, like buy up assets (which he does mention and include in the ""print money"" category of things that can be done during a deleveraging).  And one of the deleveragings he cites, England in the 1950s, according to Wikipedia was due to difficulty in transitioning out from war production, and according to [this excel file](http://www.bankofengland.co.uk/statistics/Documents/rates/baserate.xls) from the Bank of England on historical rates, it doesn't say interest rates went to 0 at that time (unless Dalio is referring to another point in history when he cites 1950s England).    20:30 His definition of a depression is when debt restructuring or defaults happen.  Interesting.  What I learned was that there isn't really a hard and fast definition for recessions and depressions (e.g. a recession is two quarters of negative growth in a row and a depression is just a reeeaallly bad/long recession).  And I don't think I recall encountering in the past an attempt to define what a ""deleveraging"" event of an economy is.    24:30 Is debt reduction and redistribution of wealth deflationary?  I think it depends on how much the debt reduction or redistribution hurts the spending of the lender or wealthy versus how much it helps the spending of the borrower or the poor.  Both are actually similarly ""giving some from the haves to the have nots,"" and especially redistribution of wealth is similar to fiscal spending, which is mentioned 25:30 as a valid inflationary way to try to help the economy.  26:00 Are deflationary methods (say, austerity) needed to balance out the inflationary methods (central bank buying assets and fiscal spending)?  Aren't central bank (interest rates, quantitative easing) and the government (fiscal policy) still the main things that move inflation or deflation?  I would think that debt reduction and redistribution of wealth are good when needed, but I wouldn't think you would do those things *mainly* for their (supposed, see above for my doubts) deflationary effects.    Still, a very interesting video and one of the best presented videos on a difficult subject." "This sounds like an accounting nightmare to be 100% precise.  With each payment you're going to have to track: If you can account for those, then the fair thing to do is for one person to stop paying after they have paid the amount of principal they had at the beginning of the process, or possibly after they have paid an amount equivalent to the total principal and accrued interest they would have paid if they paid their loans individually.   The problem is, one of you is likely going to pay more interest than you would have under the individual plan.  In the example you gave, if your brother pays off any of your loans, he is going to be paying more in interest than if he paid on his 5% loans. If you pay the highest rate loans first, whoever has the lower total balance is going to pay more interest since they'll be paying on the higher rates until they've paid their ""fair share"".   I don't see a clean way for you to divvy up the interest savings appropriately unless you trueup at the very end of the process.   Math aside, these types of agreements can be dangerous to relationships. What if one of you decides that they don't want to participate anymore? What if one of you gets all of their loans paid off much earlier - they get the joy of being debt free while the other still has all of the debt left? What if they then don't feel obligates to pay the other's remaining debt? Are you both equally committed to cutting lifestyle in order to attack these debts? In my opinion, the complexity and risk to the relationship don't justify the interest savings." If I recall correctly, the pay schedule is such that you initially pay mostly interest.  As James Roth suggests, look at the terms of the loan, specifically the payment schedule.  It should detail how much is being applied to interest and how much to the actual balance.