How does Value get rounded in figuring out Bonds Value?
With the formula you are using you assume that the issued bond (bond A) is a perpetual. Given the provided information, you can't really do more than this, it's only an approximation.  The difference could be explained by the repayment of the principal (which is not the case with a perpetual). I guess the author has calculated the bond value with principal repayment.  You can get more insight in the calculation from the excel provided at this website: http://breakingdownfinance.com/finance-topics/bond-valuation/fixed-rate-bond-valuation/
Rating agencies should be paid on accuracy, i.e. each bond issued pays x $ into a pool, and the bond companies whom are accurate over the maturity get a share of the pool.  Those whom are not, must add money to the pool. (Like an accuracy market!) As I'm sure you are reading in Hull's classic, the basic valuation of bonds depends on the chance of entity defaulting on those bonds.  Let's start with just looking at the US.  The United States has a big advantage over corporations in issuing debt as it also prints the same currency that the debt is denominated in.  This makes it much easier not to default on your debt as you can always print more money to pay it.  Printing too much currency would cause inflation lowering the value of debt, but this would also lower the value of US corporate debt as well.  So you can think of even the highest rated corporate bonds as having the same rate as government debt plus a little extra due to the additional default risk of the corporation. The situation with other AA rated governments is more complicated.  Most of those governments have debt denominated in their local currency as well so it may seem like they should all have similar rates.  However, some governments have higher and some actually have lower rates than the United States.  Now, as above, some of the difference is due to the possible need of printing too much currency to cover the debt in crisis and now that we have more than one country to invest in the extra risk of international money flowing out of the country's bonds. However, the bigger difference between AA governments rates depends more on money flow, central banks and regulation.  Bonds are still mostly freely traded instruments that respond to supply and demand, but this supply and demand is heavily influenced by governments.  Central banks buy up large portions of the debt raising demand and lowering rates.  Regulators force banks to hold a certain amount of treasuries perhaps inflating demand. Finally, to answer your question the United States has some interesting advantages partially just due to its long history of stability, controlled inflation and large economy making treasuries valuable as one of the lowest risk investments.  So its rates are generally on the low end, but government manipulation can still mean that it is not necessarily the lowest. A bond has a duration that can be easily calculated. It's the time weighted average of all the payments you'll receive and helpful to understand the effect a change in rates will have on that instrument.  The duration of a stock, on the other hand, is a forced construct to then use in other equations to help calculate, say, the summation of a dividend stream. I can calculate the duration of a bond and come up with an answer that's not up for discussion or dispute. The duration of a stock, on the other hand, isn't such a number. Will J&J last 50 more years? Will Apple? Who knows? Investopedia has a good explanation of the term shorting which is what this is. In the simplest of terms, someone is borrowing the bond and selling it with the intent to replace the security and any dividends or coupons in the end. The idea is that if a bond is overvalued, one may be able to buy it back later for a cheaper price and pocket the difference. There are various rules about this including margin requirements to maintain since there is the risk of the security going up in price enough that someone may be forced into a buy to cover in the form of a margin call. If one can sell the bond at $960 now and then buy it back later for $952.38 then one could pocket the difference. Part of what you aren't seeing is what are other bonds doing in terms of their prices over time here. The key point here is that brokers may lend out securities and accrue interest on loaned securities for another point here. I dont really understand how this would work. In stocks, you are buying a share in a company at a specific price that fluctuates with the value of the company. In bonds, you are lending money for a specific time period with the hopes of getting your money back plus interest. Is actual money going to be lent? Are there going to be different bond products for each company every time they issue new debt? It just doesn't seem practical to me. I looked into the investopedia one (all their videos are mazing), but that detail just was not clear to me, it also makes be wonder, if a country issues bonds to finance itself, what happens at maturity when literally millions of them  need to be paid? The income needs to have grown to that level or it defaults? Wouldn't all the countries default if that was the case, or are bonds being issued to being able to pay maturity of older bonds already?  (I'm freaking myself out by realizing this) "Bob should treat both positions as incomplete, and explore a viewpoint which does a better job of separating value from volatility. So we should start by recognizing that what Bob is really doing is trading pieces of paper (say Stocks from Fund #1 or Bonds from Fund #2, to pick historically volatile and non-volatile instruments.*) for pieces of paper (Greenbacks).  In the end, this is a trade, and should always be thought of as such.  Does Bob value his stocks more than his bonds?  Then he should probably draw from Fund #2.  If he values his bonds more, he should probably draw from Fund #1. However, both Bob and his financial adviser demonstrate an assumption: that an instrument, whether stock bond or dollar bill, has some intrinsic value (which may raise over time).  The issue is whether its perceived value is a good measure of its actual value or not. From this perspective, we can see the stock (Fund #1) as having an actual value that grows quickly (6.5% - 1.85% = 4.65%), and the bond (Fund #2) as having an actual value that grows slower (4.5% - 1.15$ = 3.35$).  Now the perceived value of the stocks is highly volatile.  The Chairman of the Fed sneezes and a high velocity trader drives a stock up or down at a rate that would give you whiplash. This perspective aligns with the broker's opinion.  If the stocks are low, it means their perceived value is artificially low, and selling it would be a mistake because the market is perceiving those pieces of paper as being worth less than they actually are.  In this case, Bob wins by keeping the stocks, and selling bonds, because the stocks are perceived as undervalued, and thus are worth keeping until perceptions change. On the other hand, consider the assumption we carefully slid into the argument without any fanfare: the assumption that the actual value of the stock aligns with its historical value.  ""Past performance does not predict future results.""  Its entirely possible that the actual value of the stocks is actually much lower than the historical value, and that it was the perceived value that was artificially higher.  It may be continuing to do so... who knows how overvalued the perceived value actually was!  In this case, Bob wins by keeping the bonds.  In this case, the stocks may have ""underperformed"" to drive perceptions towards their actual value, and Bob has a great chance to get out from under this market. The reality is somewhere between them.  The actual values are moving, and the perceived values are moving, and the world mixes them up enough to make Scratchers lottery tickets look like a decent investment instrument.  So what can we do? Bob's broker has a smart idea, he's just not fully explaining it because it is unprofessional to do so.  Historically speaking, Bobs who lost a bunch of money in the stock market are poor judges of where the stock market is going next (arguably, you should be talking to the Joes who made a bunch of money. They might have more of a clue.).  Humans are emotional beings, and we have an emotional instinct to cut ties when things start to go south.  The market preys on emotional thinkers, happily giving them what they want in exchange for taking some of their money.  Bob's broker is quoting a well recognized phrase that is a polite way of saying ""you are being emotional in your judgement, and here is a phrasing to suggest you should temper that judgement."" Of course the broker may also not know what they're doing!  (I've seen arguments that they don't!)  Plenty of people listened to their brokers all the way to the great crash of 2008.  Brokers are human too, they just put their emotions in different places.  So now Bob has no clear voice to listen to.  Sounds like a trap! However, there is a solution.  Bob should think about more than just simple dollars.  Bob should think about the rest of his life, and where he would like the risk to appear.  If Bob draws from Fund #1 (liquidating stocks), then Bob has made a choice to realize any losses or gains early... specifically now.  He may win, he may lose.  However, no matter what, he will have a less volatile portfolio, and thus he can rely on it more in the long run. If Bob draws from Fund #2 (liquidating bonds) instead, then Bob has made a choice not to realize any losses or gains right away.  He may win, he may lose.  However, whether he wins or loses will not be clear, perhaps until retirement when he needs to draw on that money, and finds Fund #1 is still under-performing, so he has to work a few more years before retirement.  There is a magical assumption that the stock market will always continue rewarding risk takers, but no one has quite been able to prove it! Once Bob includes his life perspective in the mix, and doesn't look just at the cold hard dollars on the table, Bob can make a more educated decision.  Just to throw more options on the table, Bob might rationally choose to do any one of a number of other options which are not extremes, in order to find a happy medium that best fits Bob's life needs: * I intentionally chose to label Fund #1 as stocks and Fund #2 as bonds, even though this is a terribly crude assumption, because I feel those words have an emotional attachment associated to them which #1 and #2 simply do not.  Given that part of the argument is that emotions play a part, it seemed reasonable to dig into underlying emotional biases as part of my wording.  Feel free to replace words as you see fit to remove this bias if desired." "You are asking multiple questions here, pieces of which may have been addressed in other questions.  A bond (I'm using US Government bonds in this example, and making the 'zero risk of default' assumption) will be priced based on today's interest rate. This is true whether it's a 10% bond with 10 years left (say rates were 10% on the 30 yr bond 20 years ago) a 2% bond with 10 years, or a new 3% 10 year bond.  The rate I use above is the 'coupon' rate, i.e. the amount the bond will pay each year in interest. What's the same for each bond is called the ""Yield to Maturity."" The price adjusts, by the market, so the return over the next ten years is the same.  A bond fund simply contains a mix of bonds, but in aggregate, has a yield as well as a duration, the time-and-interest-weighted maturity.  When rates rise, the bond fund will drop in value based on this factor (duration). Does this begin to answer your question?" Okay let's try this a different way. Completely forget about what the bond is with. Here is how a bond works:   * You get paid interest for holding the bond (5% interest means a coupon of $50 assuming one coupon a year)    * At the end of the bond term (maturity) you get paid $1000.     In your scenario, you get paid the $50 as an interest payment and the $1000 final payment.    If you only had the bond for one year, your total payment will be $1050.     Try drawing a timeline to visualise it a bit better "The answer to almost all questions of this type is to draw a diagram.  This will show you in graphical fashion the timing of all payments out and payments received.  Then, if all these payments are brought to the same date and set equal to each other (using the desired rate of return), the equation to be solved is generated. In this case, taking the start of the bond's life as the point of reference, the various amounts are: Pay out = X Received = a series of 15 annual payments of $70, the first coming in 1 year.  This can be brought to the reference date using the formula for the present value of an ordinary annuity. PLUS Received = A single payment of $1000, made 15 years in the future.  This can be brought to the reference date using the simple interest formula. Set the pay-out equal to the present value of the payments received and solve for X I am unaware of the difference, if any, between ""current rate"" and ""rate to maturity"" Finding the rate for such a series of payments would start out the same as above, but solving the resulting equation for the interest rate would be a daunting task..." In this case the market interest rate is the discount rate that sets equal the market price (current value) of the bond to its present value. To find the market interest rate which is also referred to as promised yield YTM you would have solve for the interest rate in the bond price formula A market price of bond is the sum of discounted coupons and the terminal value of the bond. Most spreadsheet programs and calculators have a RATE function that makes possible finding this market interest rate. First see this for finding a coupon paying bond price The coupon payments are discounted so is the par value of the bond and sum of such discounts is the market price of the bond. The TVM functions in Excel and calculators make this possible using the following equation Let us take your data, 9% $100,000 coupon with 5 years remaining to maturity with market interest rate of 10%. Bonds issued in the US mostly pay two coupons per year. Thus we are finding the present value of 10 coupons each worth $4500 and par value of $100,000. The semi-annual market interest rate is 10%/2 or 5% The negative sign indicate money going out of hand Now solving for RATE is only possible using numerical methods and the RATE function is programmed using Newton-Raphson method to find one of the roots of the bond price equation. This rate will be the periodic rate in this case semi-annual rate which you have to multiply by 2 to get the annual rate. Do remember there is a difference between annual nominal rate and an annualized effective rate. To find the market interest rate  If you don't have Excel or a financial calculator then you may opt to use my version of these financial functions in this JavaScript library tadJS Bonds have multiple points of risk: This is part of the time value of money chapter in any finance course.  Disclaimer - Duff's answer popped up as I was still doing the bond calculations. Similar to mine but less nerdy. "You ask two questions - First - the market value can drop for two reasons (that I know), the company itself may have issues, and investors don't trust they'll be paid, or a general rise in interest rates. In the latter case, there's little to worry about, but for the former, well, that's your decision, you say ""the company is in trouble"" yet you believe they'll pay. Tough call. Second - yes, when a bond matures, the money appears in your account." If you have two other assets whose payoffs tomorrow are known and whose prices today are known, you can value it.  Let's say you can observe a risk-free bond and a stock. Using those, you can calculate the state prices/risk-neutral probabilities. NOTE: You do not need to know the true probabilities.   The value of your asset is then the state-price weighted sum of future payoffs. "Of course it can. This is a time value of money calculation. If I knew the maturity date, or current yield to maturity I'd be able to calculate the other number and advise how much rates need to rise to cause the value to drop from 18 to 17. For a 10 year bond, a rise today of .1% will cause the bond to drop about 1% in value. This is a back of napkin calculation, finance calculators offer precision. edit - when I calculate present value with 34 years to go, and 5.832% yield to maturity, I get $14.55. At 5.932, the value drops to $14.09, a drop of 3.1%.  Edit - Geo asked me to show calculations. Here it goes - A) The simplest way to calculate present value for a zero coupon bond is to take the rate 5.832%, convert it to 1.05832 and divide into the face value, $100. I offer this as the ""four function calculator"" approach, so one enters $100 divided by 1.05832 and repeat for the number of years left. A bit of precision is lost if there's a fractional year involved, but it's close. The bid/ask will be wider than this error introduced.  B) Next - If you've never read my open declaration of love for my Texas Instruments BA-35 calculator, here it is, again. One enters N=34 (for the years) FV = 100, Rate = 5.832, and then CPT PV. It will give the result, $14.56.  C) Here is how to do it in Excel -  The numbers in lines 1-3 are self evident, the equation in cell B4 is =-PV(B3/100,B1,0,B2) - please note there are tiny differences in the way to calculate in excel vs a calculator. Excel wants the rate to be .05832, so I divided by 100 in the equation cell.  That's the best 3 ways I know to calculate present value. Geo, if you've not noticed, the time value of money is near and dear to me. It comes into play for bonds, mortgages, and many aspect of investing. The equations get more complex if there are payments each year, but both the BA-35 and excel are up to it."