What is a Discount Called in the Context of a Negative Interest Rate?
"Even though the article doesn't actually use the word ""discount"", I think the corresponding word you are looking for is ""premium"". The words are used quite frequently even outside of the context of negative rates. In general, bonds are issued with coupons close to the prevailing level of interest rates, i.e. their price is close to par (100 dollar price). Suppose yields go up the next day, then the price moves inversely to yields, and that bond will now trade at a ""discount to par"" (less than 100 dollar price). And vice versa, if yields went down, prices go up, and the bond is now at a ""premium to par"" (greater than 100 dollar price)" "Negative Yields on Bonds is opposite of Getting profit on your investment. This is some kind of new practice from world wide financial institute.  the interest rate is -0.05% for ten years. So a $100,000 bond under   those terms would be ""discounted"" to $100,501, give or take. No, actually what you are going to get out from this investment is after 10 years when this investment is mature for liquidation, you will get return not even your principle $100,000 , but ( (Principle $100,000) minus (Negative Yields @ -0.05) Times ( 10 Years ) ) assume the rates are on simple annual rate.  Now anyone may wander why should someone going to buy this kind of investment where I am actually giving away not only possible profit also losing some of principle amount!  This might looks real odd, but there is other valid reason for issuing / investing on such kind of bond.  From investor prospective: Every asset has its own 'expense' for keeping ownership of it. This is also true for money/currency depending on its size. And other investment possibility and risk factor. The same way people maintain checking account with virtually no visible income vs. Savings account where bank issue some positive rate of interest with various time factor like annually/half-yearly/monthly. People with lower level of income but steady on flow choose savings where business personals go for checking one. Think of Millions of Ideal money with no secure investment opportunity have to option in real. Option one to keeping this large amount of money in hand, arranging all kind of security which involve extra expense, risk and headache where Option two is invest on bond issued by Government of country. Owner of that amount will go for second one even with negative yields on bonds where he is paying in return of security and risk free grantee of getting it back on time.  On Issuing Government prospective: Here government actually want people not to keep money idle investing bonds, but find any possible sector to invest which might profitable for both Investor + Grater Community ultimately country.  This is a basic understanding on issue/buy/selling of Negative interest bearing bond on market.   Hope I could explain it here. Not to mention, English is not my 1st language at all. So ignore my typo, grammatical error and welcome to fix it.  Cheers!"
Right, I understand minority interest but it is typically reported as a positive under liabilities instead of a negative. For example, when you are calculating the enterprise value of a company, you add back in the minority interest.    Enterprise Value= Market Share +Pref Equity + Min Interest+ Total Debt - Cash and ST Equivalents.    EV is used to quantify the total price of a company's worth. If you have negative Min Interest on your books, that will make your EV less than it should be, creating an incorrect valuation.   This just doesn't make any sense to me. Does it mean that the subsidiary that they had a stake in had a negative earning? Savings accounts have limitations in case a bank goes belly up and you have a higher amount in the account (more than the insured amount). Mostly big corporations or pension funds cannot rely on a bank to secure their cash but a government bond is secured (with some fine print) and hence they are willing to take negative interest rates. There is no interest outstanding, per se.  There is only principal outstanding.  Initially, principal outstanding is simply your initial loan amount. The first two sections discuss the math needed - just some arithmetic. The interest that you owe is typically calculated on a monthly basis.  The interested owed formula is simply (p*I)/12, where p is the principal outstanding, I is your annual interest, and you're dividing by 12 to turn annual to monthly. With a monthly payment, take out interest owed.  What you have left gets applied into lowering your principal outstanding.  If your actual monthly payment is less than the interest owed, then you have negative amortization where your principal outstanding goes up instead of down. Regardless of how the monthly payment comes about (eg prepay, underpay, no payment), you just apply these two calculations above and you're set.  The sections below will discuss these cases in differing payments in detail. For a standard 30 year fixed rate loan, the monthly payment is calculated to pay-off the entire loan in 30 years.  If you pay exactly this amount every month, your loan will be paid off, including the principal, in 30 years.  The breakdown of the initial payment will be almost all interest, as you have noticed.  Of course, there is a little bit of principal in that payment or your principal outstanding would not decrease and you would never pay off the loan. If you pay any amount less than the monthly payment, you extend the duration of your loan to longer than 30 years.  How much less than the monthly payment will determine how much longer you extend your loan.  If it's a little less, you may extend your loan to 40 years.  It's possible to extend the loan to any duration you like by paying less.  Mathematically, this makes sense, but legally, the loan department will say you're in breach of your contract. Let's pay a little less and see what happens.  If you pay exactly the interest owed = (p*I)/12, you would have an infinite duration loan where your principal outstanding would always be the same as your initial principal or the initial amount of your loan.   If you pay less than the interest owed, you will actually owe more every month.  In other words, your principal outstanding will increase every month!!!  This is called negative amortization.  Of course, this includes the case where you make zero payment.  You will owe more money every month. Of course, for most loans, you cannot pay less than the required monthly payments.  If you do, you are in default of the loan terms. If you pay more than the required monthly payment, you shorten the duration of your loan.  Your principal outstanding will be less by the amount that you overpaid the required monthly payment by.  For example, if your required monthly payment is $200 and you paid $300, $100 will go into reducing your principal outstanding (in addition to the bit in the $200 used to pay down your principal outstanding).  Of course, if you hit the lottery and overpay by the entire principal outstanding amount, then you will have paid off the entire loan in one shot! When you get to non-standard contracts, a loan can be structured to have any kind of required monthly payments.  They don't have to be fixed.   For example, there are Balloon Loans where you have small monthly payments in the beginning and large monthly payments in the last year.   Is the math any different?  Not really - you still apply the one important formula, interest owed = (p*I)/12, on a monthly basis.  Then you break down the amount you paid for the month into the interest owed you just calculated and principal.  You apply that principal amount to lowering your principal outstanding for the next month. Supposing that what you have posted is accurate, the most likely scenario is that you have a structured 5 year car loan where your monthly payments are smaller than the required fixed monthly payment for a 5 year loan, so even after 2 years, you owe as much or more than you did in the beginning!  That means you have some large balloon payments towards the end of your loan.  All of this is just part of the contract and has nothing to do with your prepay. Maybe I'm incorrect in my thinking, but I have a question about   prepaying a loan. When you take out a mortgage on a home or a car   loan, it is my understanding that for the first years of payment you   are paying mostly interest. Correct. So, let's take a mortgage loan that allows prepayment without penalty.   If I have a 30 year mortgage and I have paid it for 15 years, by the   16th year almost all the interest on the 30 year loan has been paid to   the bank and I'm only paying primarily principle for the remainder of   the loan. Incorrect.  It seems counter-intuitive, but even in year 16, about 53% of your monthly payment still goes to interest!!!  It is hard to see this unless you try to do the calculations yourself in a spreadsheet. If suddenly I come into a large sum of money and decide I want to pay   off the mortgage in the 16th year, but the bank has already received   all the interest computed for 30 years, shouldn't the bank recompute   the interest for 16 years and then recalculate what's actually owed in   effect on a 16 year loan not a 30 year loan? It is my understanding   that the bank doesn't do this. What they do is just tell you the   balance owed under the 30 year agreement and that's your payoff   amount. Your last sentence is correct.  The payoff amount is simply the principal outstanding plus any interest from (p*I)/12 that you owe.  In your example of trying to payoff the rest of your 30 year loan in year 16, you will owe around 68% of your original loan amount. That seems unfair. Shouldn't the loan be recalculated as a 16 year   loan, which it actually has become? In fact, you do have the equivalent of a 15 year loan (30-15=15) at about 68% of your initial loan amount.  If you refinanced, that's exactly what you would see.  In other words, for a 30y loan at 5% for $10,000, you have monthly payments of $53.68, which is exactly the same as a 15y loan at 5% for $6,788.39 (your principal outstanding after 15 years of payments), which would also have monthly payments of $53.68. A few years ago I had a 5 year car   loan. I wanted to prepay it after 2 years and I asked this question to   the lender. I expected a reduction in the interest attached to the car   loan since it didn't go the full 5 years. They basically told me I was   crazy and the balance owed was the full amount of the 5 year car loan.   I didn't prepay it because of this. That is the wrong reason for not prepaying.  I suspect you have misunderstood the terms of the loan - look at the Variable Monthly Payments section above for a discussion.   The best thing to do with all loans is to read the terms carefully and do the calculations yourself in a spreadsheet.  If you are able to get the cashflows spelled out in the contract, then you have understood the loan. I see another way of looking at this that hasn't been addressed yet. By offering the discount, the company is attempting to change your behavior into doing something irrational, that benefits them at your expense. The company hopes for one (or more) of the following psychological effects to happen to you: The proper thing to do, if you have enough capital to prevent margin calls, it to short-sell the stock at the same instant the price is set, thus locking in the profit. Eventually you can take possession of the shares and deliver them to offset the short -- hopefully before you get a margin call from the stock dropping. "These rates are so low because the cost of money is so low. Specifically, two rates are near zero.  The Federal Reserve discount rate, which is ""the interest rate charged to commercial banks and other depository institutions on loans they receive from their regional Federal Reserve Bank's lending facility--the discount window."" The effective federal funds rate, which is the rate banks pay when they trade balances with each other through the Federal Reserve. Banks want to profit on the loans they make, like mortgage loans. To do so, they try to maximize the difference between the rates they charge on mortgages and other loans (revenue), and the rates they pay savings account holders, the Federal Reserve or other banks to obtain funds (expenses). This means that the rates they offer to pay are as close to these rates as possible. As the charts shows, both rates have been cut significantly since the start of the recession, either through open market operations (the federal funds rate) or directly (the discount rate). The discount rate is set directly by the regional Federal Reserve banks every 14 days.   In most cases, the federal funds rate is lower than the discount rate, in order to encourage banks to lend money to each other instead of borrowing it from the Fed. In the past, however, there have been rare instances where the federal funds rate has exceeded the discount rate, and it's been cheaper for banks to borrow money directly from the Fed than from each other." Yes those are really yields. A large portion of the world has negative yielding bonds in fact. This process has been in motion for the past 10 years for very specific reasons. So congratulations on discovering the bond market. "It makes sense if the NPV is positive. But what rate should you use at determining the NPV? A textbook might say ""market rate"".... and by definition the market rate to use in bond calculations like yours will mean that your NPV will be zero.  How can this be? Well it's a bit of a circular definition. You take less capital to earn a higher return. The value of your capital spread over the period of the bond's maturity is the net difference... but the money in your pocket from selling the bond and not purchasing also has value. Banks and traders do this exact swap every day, many many times. The rate at which you can execute this swap is what defines the market rate. Therefore, by definition, the NPV will be zero. Now, this doesn't mean it's a bad idea for you. You can, on your own accord, decide the value you place on the capital versus the yield and make the decision. Do you expect rates to rise or fall? Do you expect higher or lower inflation? In reality you can form whatever opinion you like for your own circumstance, but the market is the net aggregation of formative opinion. You only get to decide whether or not you agree with the market." I know this can be confusing because you tend to think of money being worth the face value. So let's eliminate that for the sake of an example that will be easier to understand. Let's say your friend loaned you rock worth $10 today. He expects you to pay him back an identical rock whenever you can. Now let's also assume that historically the price of rocks tends to go down every year. At some point you will need to buy a rock to pay your friend back. Because they keep getting cheaper, it costs less to buy the payback rock the longer you wait. Replace a dollar with a rock in the example and you have your answer. This is known as the time value of money. In reality, this is priced into the loan (via the interest rate) because the lender very much understands the math going on here. Also, it is more complicated because the longer you delay payment the more interest you pay (pebbles if you will) so it doesn't usually work to your advantage unless they underpriced the loan's interest rate. Supply and demand for a particular bond may be such that the market price exceeds the par value for the bond at maturity. This is when you get a negative yield. Especially when volatility is high, people will actually pay money to park it in treasuries for an amount of time. But when compared to a > 25% vol in the equities market over that same period, taking a 5% or less hit doesn't sound nearly as bad! "I would say people are generally talking about the prime lending rate. I have heard the prime lending rate defined as ""The rate that banks charge each other when they borrow money overnight."" But it often defined as the rate at which banks lend their most creditworthy customers. That definition comes with the caveat that it is not always held to strictly. Either definition has the same idea: it's the lowest rate at which anyone could currently borrow money. The rate for many types of lending is based upon the prime rate. A variable rate loan might have an interest rate of (Prime + x). The prime rate is in turn based upon the Federal Funds Rate, which is the rate that the Fed sets manually. When the news breaks that ""the Fed is raising interest rates by a quarter of a point""  (or similar) it is the Federal Funds Rate that they control. Lending institutions then ""fall in line"" and adjust the rates at which they lend money. So to summarize: When people refer to ""high"" or ""low"" or ""rising"" interest rates they are conceptually referring to the prime lending rate. When people talk about the Fed raising/lowering interest rates (In the U.S.) they are referring specifically to the Federal Funds Rate (which ultimately sets other lending rates)." for buying: High PE, low debt, discount = win. a company with high debt (in relation to revenues and cash on hand) will have to pay interest and pay off the debt, stunting their growth. and just like a normal person, will barely be able to pay their bills and keep borrowing and might go bankrupt determining discount is just looking for a technical retracement to a support level or lower. (but if you dont enter at the support level, you most likely missed the best entry) Your mortgage represents a negative cash flow of $X for N months. The typical mortgage prepayment doesn't reduce your next payment, but does reduce the length of the mortgage. If you look at the amortization table of a 30 year loan, you might see a payment of $1000 but only $50 going to principal. So if on day one you send an extra $51 or so to the bank, you find that in 30 years you just saved that $1000 payment. In effect, it was a long term bond or CD, yielding the post tax rate of the mortgage. Say your loan were 7%. At 7%, money doubles every 10 years or so. 30 years is 3 doubles or 8X. If I were to offer you $1000 and ask for $7500 in 30 years, you might accept it, with an agreement to buy me out if you refinanced. For me, that would be an investment. Just like buying a bond. In fact, there is a real return, as you see the cash flow at the end. The payments 'not made' are your payback.  Those who insist it's not an investment are correct in the strict sense of the word's definition, but pedantic for the fact in practice, the prepayment is a choice to be considered alongside other investment choices. When I have a mortgage, I am the mortgagor, the bank, the mortgagee. Same as a company issuing a bond, the Bank holds my bond and I'm making payments to them. They hold my bond as an investment. There is no question of that. In fact, they package these and sell them as CMOs, groups of mortgages. A pre-payment is me buying back the last coupon on my mortgage. I fail to see the distinction between me 'buying back' $10K in future coupons on my own loan or me investing $10K in someone else's loans.  The real question for me is whether this makes sense when rates are so low. At 4%, I'd say it's a matter of prioritizing any high rate debt and any other investments that might yield more. But even so, it's an investment yielding 4%.  Over the years, I've developed the priorities of where to put new money - The priorities are debatable. I have my opinion, and my reasons to back them up. In general, it's a balance between risk and return. In my opinion, there's something wrong with ignoring a dollar for dollar match on the 401(k) in most circumstances. Others seem to prefer being 100% debt free before saving at all. There's a balance that might be different for each individual. As I started, the mortgage is a fixed return, with no chance to just get it back if needed. If your cash savings is pretty high, and the choice is a .001% CD or prepay a 4% mortgage, I'd use some funds to pay it down. But not to the point you have no liquid reserves. There is another reason why an investor might buy negative yielding bonds: if the investor expects that bond yields will go even further negative, then they are also expecting the price of the bond to go up. They can resell the bond later at a profit. As an example, they may expect an increase in central bank bond purchases to drive yields lower and prices higher. Part 2 = 12%  -5000/0.12 (1 - 1/(1.12^2 ) = -8450.26 Then subtract year 0s 5000 payment if you havent = -13450.26 and then compare to option 2 -2000/0.12 (1 - 1/(1.12^10) = -11300.46 and subtract 20000 -31300.46  As you can see both values are substantially smaller compared to a 4% discount rate. I haven't read the terms here but the question may not have a good answer.  That won't stop me from trying.   Call the real rate (interest rate - inflation) and you'll have what is called negative real rates. It's rare for the overnight real rate to be negative.  If you check the same sources for historical data you'll find it's usually higher.  This is because borrowing money is usually done to gain an economic benefit, ie. make a profit.  That is no longer a consideration when borrowing money short term and is IMO a serious problem.  This will cause poor investment decisions like you see in housing. Notice I said overnight rate.  That is the only rate set by the BoC and the longer rates are set by the market.  The central bank has some influence because a longer term is just a series of shorter terms but if you looked up the rate on long Canadian real return bonds, you'd see them with a real rate around 1%. What happens when the central bank raise or lowers rates will depend on the circumstances.  The rate in India is so high because they are using it to defend the rupee.  If people earn more interest they have a preference to buy that currency rather than others.  However these people aren't stupid, they realize it's the real rate that matters.  That's why Japan can get away with very low rates and still have demand for the currency - they have, or had, deflation.  When that changed, the preference for their currency changed. So if Canada hast forex driven inflation then the BoC will have to raise rates to defend the dollar for the purpose of lowering inflation from imports.  Whether it works or not is another story.  Note that the Canadian dollar is very dependant on the total dollar value of net oil exports. If Canada has inflation due too an accelerating economy this implies that there are profitable opportunities so businesses and individuals will be more likely to pay a positive real rate of interest.  In that scenario the demand for credit money will drive the real rate of return.