How are mortgage interest rates determined?
Mortgage or other interest rates are determined by the banks on cost of funds, risk and operating cost.   The Fed raises money from the markets by issuing Tresury Bonds at a specified rate. This rate at which it raises money varies depening on the economy. Thus there are 2 rates: the rate at which banks can borrow money from the Fed, which is higher than the rate that the Fed would give banks for excess money deposited with them. So if the cost of borrowing is less, banks can borrow this money from the Fed and loan it to individuals at a slightly higher rate that would cover their costs plus a small profit. The risk associated with a mortgage is less, and hence these would be cheaper, then say a personal loan.  If the cost of borrowing goes up, the mortgage rate will go up. If the cost of borrowing money goes down, the cost would come down. Banks may not always borrow money to lend. If they have existing money, they can either park it with the Fed for a lower interest rate, or loan it to individuals for a rate higher than what they would have received from the Fed. One will find that the fixed 30 year mortgage rate is tightly correlated to the 10 year treasury. An adder of 2-2.5% or so, changing slightly with the rest of the economy, as money can get tight or loose independent of the rate itself. In 2011 we are witnessing low rates yet tough loan standards, this is the phenomenon I am referencing. Sheegan has a great explanation of how the TBA market contributes to  mortgage rates. The 30 Year Mortgage rates are closely tied to the 10-Year Treasury.  One can track this rate at many stock quoting sites using symbol TNX.
The reason it's broken out is very specific: this is showing you how much interest accrued during the month.  It is the only place that's shown, typically. Each month's (minimum) payment is the sum of [the interest accrued during that month] and [some principal], say M=I+P, and B is your total loan balance.  That I is fixed at the amount of interest that accrued that month - you always must pay off the accrued interest.  It changes each month as some of the principal is reduced; if you have a 3% daily interest rate, you owe (0.03*B*31) approximately (plus a bit as the interest on the interest accrues) each month (or *30 or *28).  Since B is going down constantly as principal is paid off, I is also going down. The P is most commonly calculated based on an amortization table, such that you have a fixed payment amount each month and pay the loan off after a certain period of time.  That's why P changes each month - because it's easier for people to have a constant monthly payment M, than to have a fixed P and variable I for a variable M. As such, it's important to show you the I amount, both so you can verify that the loan is being correctly charged/paid, and for your tax purposes. As of now in 2016, is is safe to assume that mortgage rates would/should not get back to 10%? What would the rates be in future is speculation. It depends on quite a few things, overall economy, demand / supply, liquidity in market etc ... Chances are less that rates would show a dramatic rise in near future. Does this mean that one should always buy a house ONLy when mortgage rates are low? Is it worth the wait IF the rates are high right now? Nope. House purchase decision are not solely based on interest rates. There are quite a few other aspects to consider, the housing industry, your need, etc. Although interest rate do form one of the aspect to consider specially affordability of the EMI.  Is refinancing an option on the table, if I made a deal at a bad time when rates are high? This depends on the terms of current mortgage. Most would allow refinance, there may be penal charges breaking the current mortgage. Note refinance does not always mean that you would get a better rate. Many mortgages these days are on variable interest rates, this means that they can go down or go up. How can people afford 10% mortgage? Well if you buy a small cheaper [Less expensive] house you can afford a higher interest rate. It's easiest to get your payment from the PMT function in Excel or Google Sheets.  So a $100,000 30 year mortgage at 3% looks like this: The basic calculation is pretty simple.  You take the annual interest rate, say 3%, divided by 12, times the existing principal balance: The idea is that borrowers would like to have a predictable payment.  The earlier payments are proportionally more interest than principal than later payments are but that's because there is much more principal outstanding on month 1 than on month 200. I have answered your question in detail here https://stackoverflow.com/questions/12396422/apr-calculation-formula The annuity formula in FDIC document is at first finding PVIFAD present value annuity due factor and multiplying it with annuity payment and then dividing it by an interest factor of (1+i) to reduce the annuity to an ordinary annuity with end of period payments They could have simply used PVIFA and multiplying it with annuity payment to find the present value of an ordinary annuity In any case, you should not follow the directions in FDIC document to find interest rate at which the present value of annuity equals the loan amount. The method they are employing is commonly used by Finance Professors to teach their students how to find internal rate of return. The method is prone to lengthy trial and error attempts without having any way of knowing what rate to use as an initial guess to kick off the interest rate calculations So this is what I would suggest if you are not short on time and would like to get yourself familiar with numerical methods or iterative techniques to find internal rate of return There are way too many methods at disposal when it comes to finding interest rates some of which include All of the above methods use a seed value as a guess rate to start the iterative calculations and if results from successive calculations tend to converge within a certain absolute Error bound, we assume that one of the rates have been found as there may be as many rates as the order of the polynomial in this case 36 There are however some other methods that help find all rates by making use of Eigenvalues, but for this you would need a lengthy discourse of Linear Algebra One of the methods that I have come across which was published in the US in 1969 (the year I was born :) ) is called the Jenkins Traub method named after the two individuals who worked jointly on finding a solution to all roots of a polynomial discarding any previous work on the same subject I been trying to go over the Jenkins Traub algorithm but am having difficulty understanding the complex nature of the calculations required to find all roots of the polynomial In summary you would be better of reading up on this site about the Newton Raphson method to find IRR "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..." "Banks make money on load origination fees. The ""points"" you pay or closing costs are the primary benefit to the banks. A vast majority of the time risks associated with the mortgage are sold to another party. FYI, the same is true with investment banks. In general, the transaction costs (which are ignored by modern finance theory) are the main thing running the incentives for the industry." "To understand the Twist, you need to understand what the Yield Curve is.  You must also understand that the price of debt is inverse to the interest rate. So when the price of bonds (or notes or bills) rises, that means the current price goes up, and the yield to maturity has gone down.  Currently (Early 2012) the short term rate is low, close to zero. The tools the fed uses, setting short term rates for one, is exhausted, as their current target is basically zero for this debt. But, my mortgage is based on 10yr rates, not 1 yr, or 30 day money. The next step in the fed's effort is to try to pull longer term rates down. By buying back 10 year notes in this quantity, the fed impacts the yield at that point on the curve. Buying (remember supply/demand) pushes the price up, and for debt, a higher price equates to lower yield. To raise the money to do this, they will sell short term debt. These two transactions effectively try to ""twist"" the curve to pull long term rates lower and push the economy." "I am trying to set up a formula that will find interest-rate behind first pencil sheets at car dealerships. I am not a car finance expert so I need someone who is intimate with how these loans really work.   The points of data I get at first pencil are: 1) Amount Financed 2) Period 3) Monthly Payment  The data I need to extrapolate: 1) Rate in percentile so that I can compare to my bank's offer.  I have tried this and many other stock ""find rate"" formulas with no accurate results: R=(A/P^(1/n)-1)n" In the US, our standard fixed rate mortgages would show no difference. My payment is calculated to be due on the 1st of each month.  When I first got a mortgage, I was intrigued by this question, and experimented. I paid early, on the 15th, 2 weeks early, and looked at my next statement. It matched the amortization, exactly. Mortgages at the time were over 12%, so I'd imagine having seen the benefit of that 1/2% for the early payment.  Next I paid on the last day before penalty, in effect, 2 weeks late. I expected to see extra interest accrue, again, just a bit, but enough to see when compared to the amortization table. Again, no difference, the next statement showed the same value to the penny. Your calculations are correct if you use the same mortgage rate for both the 15 and 30 year mortgages.  However, generally when you apply for a 15 year mortgage the interest rate is significantly less than the 30 year rate.  The rate is lower for a number of reasons but mainly there is less risk for the bank on a 15 year payoff plan. You’ve really got three or four questions going here… and it’s clear that a gap in understanding one component of how bonds work (pricing) is having a ripple effect across the other facets of your question. The reality is that everybody’s answers so far touch on various pieces of your general question, but maybe I can help by integrating. So, let’s start by nailing down what your actual questions are:  1. Why do mortgage rates (tend to) increase when the published treasury bond rate increases? I’m going to come back to this, because it requires a lot of building blocks. 2. What’s the math behind a bond yield increasing (price falling?)  This gets complicated, fast. Especially when you start talking about selling the bond in the middle of its time period. Many people that trade in bonds use financial calculators, Excel, or pre-calculated tables to simplify or even just approximate the value of a bond. But here’s a simple example that shows the math.  Let’s say we’ve got a bond that is issued by… Dell for $10,000. The company will pay it back in 5 years, and it is offering an 8% rate. Interest payments will only be paid annually. Remember that the amount Dell has promised to pay in interest is fixed for the life of the bond, and is called the ‘coupon’ rate. We can think about the way the payouts will be paid in the following table:   As I’m sure you know, the value of a bond (its yield) comes from two sources: the interest payments, and the return of the principal. But, if you as an investor paid $14,000 for this bond, you would usually be wrong. You need to ‘discount’ those amounts to take into account the ‘time value of money’. This is why when you are dealing in bonds it is important to know the ‘coupon rate’ (what is Dell paying each period?). But it is also important to know your sellers’/buyers’ own personal discount rates. This will vary from person to person and institution to institution, but it is what actually sets the PRICE you would buy this bond for.  There are three general cases for the discount rate (or the MARKET rate). First, where the market rate == the coupon rate. This is known as “par” in bond parlance. Second, where the market rate < the coupon rate. This is known as “premium” in bond parlance. Third, where the market rate > coupon rate. This is known as a ‘discount’ bond.  But before we get into those in too much depth, how does discounting work? The idea behind discounting is that you need to account for the idea that a dollar today is not worth the same as a dollar tomorrow. (It’s usually worth ‘more’ tomorrow.) You discount a lump sum, like the return of the principal, differently than you do a series of equal cash flows, like the stream of $800 interest payments. The formula for discounting a lump sum is:  Present Value=Future Value* (1/(1+interest rate))^((# of periods)) The formula for discounting a stream of equal payments is:  Present Value=(Single Payment)* (〖1-(1+i)〗^((-n))/i) (i = interest rate and n = number of periods) **cite investopedia So let’s look at how this would look in pricing the pretend Dell bond as a par bond. First, we discount the return of the $10,000 principal as (10,000 * (1 / 1.08)^5). That equals $6,807.82.  Next we discount the 5 equal payments of $800 as (800* (3.9902)). I just plugged and chugged but you can do that yourself. That equals $3,192.18. You may get slightly different numbers with rounding.  So you add the two together, and it says that you would be willing to pay ($6,807.82 + $3,192.18) = $10,000. Surprise! When the bond is a par bond you’re basically being compensated for the time value of money with the interest payments. You purchase the bond at the ‘face value’, which is the principal that will be returned at the end.  If you worked through the math for a 6% discount rate on an 8% coupon bond, you would see that it’s “premium”, because you would pay more than the principal that is returned to obtain the bond [10,842.87 vs 10,000]. Similarly, if you work through the math for a 10% discount rate on an 8% coupon bond, it’s a ‘discount’ bond because you will pay less than the principal that is returned for the bond [9,241.84 vs 10,000].  It’s easy to see how an investor could hold our imaginary Dell bond for one year, collect the first interest payment, and then sell the bond on to another investor. The mechanics of the calculations are the same, except that one less interest payment is available, and the principal will be returned one year sooner… so N=4 in both formulae.  Still with me? Now that we’re on the same page about how a bond is priced, we can talk about “Yield To Maturity”, which is at the heart of your main question.  Bond “yields” like the ones you can access on CNBC or Yahoo!Finance or wherever you may be looking are actually taking the reverse approach to this. In these cases the prices are ‘fixed’ in that the sellers have listed the bonds for sale, and specified the price. Since the coupon values are fixed already by whatever organization issued the bond, the rate of return can be imputed from those values.  To do that, you just do a bit of algebra and swap “present value” and “future value” in our two equations.  Let’s say that Dell has gone private, had an awesome year, and figured out how to make robot unicorns that do wonderful things for all mankind. You decide that now would be a great time to sell your bond after holding it for one year… and collecting that $800 interest payment. You think you’d like to sell it for $10,500. (Since the principal return is fixed (+10,000); the number of periods is fixed (4); and the interest payments are fixed ($800); but you’ve changed the price... something else has to adjust and that is the discount rate.) It’s kind of tricky to actually use those equations to solve for this by hand… you end up with two equations… one unknown, and set them equal. So, the easiest way to solve for this rate is actually in Excel, using the function =RATE(NPER, PMT, PV, FV). NPER = 4, PMT = 800, PV=-10500, and FV=10000. Hint to make sure that you catch the minus sign in front of the present value… buyer pays now for the positive return of 10,000 in the future.  That shows 6.54% as the effective discount rate (or rate of return) for the investor. That is the same thing as the yield to maturity. It specifies the return that a bond investor would see if he or she purchased the bond today and held it to maturity.  3. What factors (in terms of supply and demand) drive changes in the bond market? I hope it’s clear now how the tradeoff works between yields going UP when prices go DOWN, and vice versa. It happens because the COUPON rate, the number of periods, and the return of principal for a bond are fixed. So when someone sells a bond in the middle of its term, the only things that can change are the price and corresponding yield/discount rate.  Other commenters… including you… have touched on some of the reasons why the prices go up and down. Generally speaking, it’s because of the basics of supply and demand… higher level of bonds for sale to be purchased by same level of demand will mean prices go down. But it’s not ‘just because interest rates are going up and down’. It has a lot more to do with the expectations for 1) risk, 2) return and 3) future inflation. Sometimes it is action by the Fed, as Joe Taxpayer has pointed out. If they sell a lot of bonds, then the basics of higher supply for a set level of demand imply that the prices should go down. Prices going down on a bond imply that yields will go up. (I really hope that’s clear by now). This is a common monetary lever that the government uses to ‘remove money’ from the system, in that they receive payments from an investor up front when the investor buys the bond from the Fed, and then the Fed gradually return that cash back into the system over time.  Sometimes it is due to uncertainty about the future. If investors at large believe that inflation is coming, then bonds become a less attractive investment, as the dollars received for future payments will be less valuable. This could lead to a sell-off in the bond markets, because investors want to cash out their bonds and transfer that capital to something that will preserve their value under inflation. Here again an increase in supply of bonds for sale will lead to decreased prices and higher yields.  At the end of the day it is really hard to predict exactly which direction bond markets will be moving, and more importantly WHY. If you figure it out, move to New York or Chicago or London and work as a trader in the bond markets. You’ll make a killing, and if you’d like I will be glad to drive your cars for you.  4. How does the availability of money supply for banks drive changes in other lending rates?  When any investment organization forms, it builds its portfolio to try to deliver a set return at the lowest risk possible. As a corollary to that, it tries to deliver the maximum return possible for a given level of risk.  When we’re talking about a bank, DumbCoder’s answer is dead on. Banks have various options to choose from, and a 10-year T-bond is broadly seen as one of the least risky investments. Thus, it is a benchmark for other investments.  5. So… now, why do mortgage rates tend to increase when the published treasury bond yield rate increases? The traditional, residential 30-year mortgage is VERY similar to a bond investment. There is a long-term investment horizon, with fixed cash payments over the term of the note. But the principal is returned incrementally during the life of the loan.  So, since mortgages are ‘more risky’ than the 10-year treasury bond, they will carry a certain premium that is tied to how much more risky an individual is as a borrower than the US government.  And here it is… no one actually directly changes the interest rate on 10-year treasuries. Not even the Fed. The Fed sets a price constraint that it will sell bonds at during its periodic auctions. Buyers bid for those, and the resulting prices imply the yield rate. If the yield rate for current 10-year bonds increases, then banks take it as a sign that everyone in the investment community sees some sign of increased risk in the future. This might be from inflation. This might be from uncertain economic performance. But whatever it is, they operate with some rule of thumb that their 30-year mortgage rate for excellent credit borrowers will be the 10-year plus 1.5% or something. And they publish their rates. Increasing rates from .75% to 1% is an attempt to control debt.  The new 1% rate drives down demand for bonds based on the old .75% rate and drives down demand for stocks who have decrease profit because they pay more interest on debt.  This is the federal reserves primary tool controling inflation.   1% is what the banks pay to borrow money, they base their lending rates on this 1% figure.  If a person can guarantee a .75% return on money borrowed at 1%, they will opt to save and instead lend their money out at 1%. The periodic rate (here, the interest charged per month), as you would enter into a finance calculator is 9.05%. Multiply by 12 to get 108.6% or calculate APR at 182.8%. Either way it's far more than 68%.  If the $1680 were paid after 365 days, it would be simple interest of 68%. For the fact that payment are made along the way, the numbers change.  Edit - A finance calculator has 5 buttons to cover the calculations:  N = number of periods or payments %i = the interest per period PV = present value PMT = Payment per period FV= Future value In your example, you've given us the number of periods, 12, present value, $1000, future value, 0, and payment, $140. The calculator tells me this is a monthly rate of 9%. As Dilip noted, you can compound as you wish, depending on what you are looking for, but the 9% isn't an opinion, it's the math. TI BA-35 Solar. Discontinued, but available on eBay. Worth every cent.  Per mhoran's comment, I'll add the spreadsheet version.  I literally copied and pasted his text into a open cell, and after entering the cell shows,  which I rounded to 9.05%. Note, the $1000 is negative, it starts as an amount owed.  And for Dilip - 1.0905^12 = 2.8281 or 182.8% effective rate. If I am the loanshark lending this money, charging 9% per month, my $1000 investment returns $2828 by the end of the year, assuming, of course, that the payment is reinvested immediately. The 108 >> 182 seems disturbing, but for lower numbers, even 12% per year, the monthly compounding only results in 12.68% This is more a question for /r/personalfinance, but I'll answer it anyways. Just use the RATE formula in excel.   =RATE(numperiods,monthly payment,amount financed)*12  Just make sure the number of periods is in months, the payment is negative, and to multiply the whole thing by 12 to get the annual interest rate. The prime rate is actually the rate at which banks lend to consumers/businesses with the highest credit ratings.  The bank rate (more commonly known as the overnight rate) is the interest rate at which banks can borrow funds from the Bank of Canada or from each other.