# Agent San Francisco – SF residential and commercial real estate home loans and financing

Agent San Francisco – SF residential and commercial real estate home loans and financing. BRE Lic #01173770 NMLS ID: #1203203 & NMLS ID: #1425778.

Agent San Francisco – Mortgage residential and commercial real estate loans and financing. Brokers Liccensed since 1994. Agent San Francisco Mortgage has been financing real estate property in specifically The San Francisco Bay Area counties. The company finances residential and commercial property and land loans. With over 20 years of experience, We at Agent San Francisco Mortgage have a committment to excellence for our cliental. Our main goal is to provide the best loan program that is availble on the market to fit your financial objectives. Typically our goal of course it to provide you with the interest rate and reduced loan payments for you residential home, investment or commercial property that you deserve. We run your loan scenerio through hundreds of lenders programs to find the right match and fit to your loan qualifications and your needs in a real estate refinance, purchase or commercial loan. At Baytech mortgage our rates are always low and will save you money on closing cost. A simple call can save you $100’s every month and you can save$1,000’s in closing clost. Or simply fill the form below so that we can get a better idea and understanding of how we can benefit you in your financing of real estate residental or commercial property.

PURCHASE | REFINANCE LOAN QUESTIONNAIRE FORM

[toggle title=”Agent San Francisco Mortgage Home Loan Types”]
1) Before any money is spent on appraisals and credit reports we first take the time to analyze the overall qualifying factors such as the property value and equity position and value of your property cooupled with your financial status and your wants and needs. We simply run several very simple financial formulas before to better guestamate wheather its is worth for you to progress to a slightlier lengthy loan applicaiton, running of credit reports and ordering real estate appraisal reports. Other mortgage companies will charge you upfront for a credit report, run your credit report and order an appraisal, before analyzing and studying your mortgage note to figure out if a loan is feasible or possible. We dont waist your time or money in that fashion and we are careful to provide you the best service that we can.

2) Because we honor our reputation as true mortgage brokers and loan officers, We assure you that we will do our best to qualify you to get a mortgage loan program and interest rate that is competitive in San Francisco. Eventhough we focus on low rates and payments we also focus on a loan program that will server your long and short term goals. 3) We specialize in since 2002 A, B and C paper 1st, 2nd and Home Equity lines of credit (HELOC) loans and we are approved with an array of competitive main lenders and niche lenders as well. 4) Agent San Francisco Mortgage is proud to announce that we are still in business with pride knowing that all of our existing clients are still with us even through the economic down turn and mortgage collaspe. We treat our clients, their family and property with dignity, care and respect and we are careful about that as real estate is one of the most important assets in a person’s financial portfolio and life. [tabs] [tab title=”LOAN TYPES”] 3) We specialize since 2002 in A, B and C paper 1st, 2nd and Home Equity lines of credit (HELOC) loans and we are approved with an array of competitive main lenders and niche lenders as well. We Do

• FIXED  10, 15, 20, 30 40 YEARS
• COMMERCIAL LOANS
• REFINANCE RESIDENTIAL & COMMERCIAL LOANS
• PURCHASE FINANCE RESIDENTIAL & COMMERCIAL LOANS
• CONSTRUCTION LOANS
• INVESTMENT LOANS
• BRIDGE LOANS

Mortgage broker agent san francisco sf residential and commercial lending

[/tab] [tabs] [tab title=”ADJUSTABLE MORTGAGE LOANS”] Adjustable Loans An adjustable-rate mortgage (ARM) is a mortgage loan where the interest rate on the note is periodically adjusted based on a variety of indices.[1] Among the most common indices are the rates on 1-year constant-maturity Treasury (CMT) securities, the Cost of Funds Index (COFI), and the London Interbank Offered Rate (LIBOR). A few lenders use their own cost of funds as an index, rather than using other indices. This is done to ensure a steady margin for the lender, whose own cost of funding will usually be related to the index. Consequently, payments made by the borrower may change over time with the changing interest rate (alternatively, the term of the loan may change). This is not to be confused with the graduated payment mortgage, which offers changing payment amounts but a fixed interest rate. Other forms of mortgage loan include the interest only mortgage, the fixed rate mortgage, the negative amortization mortgage, and the balloon payment mortgage. Adjustable rates transfer part of the interest rate risk from the lender to the borrower. They can be used where unpredictable interest rates make fixed rate loans difficult to obtain. The borrower benefits if the interest rate falls but loses if the interest rate increases. Adjustable rate mortgages are characterized by their index and limitations on charges (caps). In many countries, adjustable rate mortgages are the norm, and in such places, may simply be referred to as mortgages. All adjustable rate mortgages have an adjusting interest rate tied to an index. In Western Europe, the index may be the ECB Refi rate (where the mortgage is called a tracker mortgage), TIBOR or Euro Interbank Offered Rate (EURIBOR). Six common indices in the United States are: * 11th District Cost of Funds Index (COFI) * London Interbank Offered Rate (LIBOR) * 12-month Treasury Average Index (MTA) * Constant Maturity Treasury (CMT) * National Average Contract Mortgage Rate * Bank Bill Swap Rate (BBSW) In some countries, banks may publish a prime lending rate which is used as the index. The index may be applied in one of three ways: directly, on a rate plus margin basis, or based on index movement. A directly applied index means that the interest rate changes exactly with the index. In other words, the interest rate on the note exactly equals the index. Of the above indices, only the contract rate index is applied directly.[1] To apply an index on a rate plus margin basis means that the interest rate will equal the underlying index plus a margin. The margin is specified in the note and remains fixed over the life of the loan.[1] For example, a mortgage interest rate may be specified in the note as being LIBOR plus 2%, 2% being the margin and LIBOR being the index. The final way to apply an index is on a movement basis. In this scheme, the mortgage is originated at an agreed upon rate, then adjusted based on the movement of the index.[1] Unlike direct or index plus margin, the initial rate is not explicitly tied to any index; the adjustments are tied to an index. Basic features of ARMs The most important basic features of ARMs are: 1. Initial interest rate. This is the beginning interest rate on an ARM. 2. The adjustment period. This is the length of time that the interest rate or loan period on an ARM is scheduled to remain unchanged. The rate is reset at the end of this period, and the monthly loan payment is recalculated. 3. The index rate. Most lenders tie ARM interest rates changes to changes in an index rate. Lenders base ARM rates on a variety of indices, the most common being rates on one-, three-, or five-year Treasury securities. Another common index is the national or regional average cost of funds to savings and loan associations. 4. The margin. This is the percentage points that lenders add to the index rate to determine the ARM’s interest rate. 5. Interest rate caps. These are the limits on how much the interest rate or the monthly payment can be changed at the end of each adjustment period or over the life of the loan. 6. Initial discounts. These are interest rate concessions, often used as promotional aids, offered the first year or more of a loan. They reduce the interest rate below the prevailing rate (the index plus the margin). 7. Negative amortization. This means the mortgage balance is increasing. This occurs whenever the monthly mortgage payments are not large enough to pay all the interest due on the mortgage. This may be caused when the payment cap contained in the ARM is low enough such that the principal plus interest payment is greater than the payment cap. 8. Conversion. The agreement with the lender may have a clause that allows the buyer to convert the ARM to a fixed-rate mortgage at designated times. 9. Prepayment. Some agreements may require the buyer to pay special fees or penalties if the ARM is paid off early. Prepayment terms are sometimes negotiable. It should be obvious that the choice of a home mortgage loan is complicated and time consuming. As a help to the buyer, the Federal Reserve Board and the Federal Home Loan Bank Board have prepared a mortgage checklist. Caps Any mortgage where payments made by the borrower may increase over time brings with it the risk of financial hardship to the borrower. To limit this risk, limitations on charges—known as caps in the industry—are a common feature of adjustable rate mortgages.[1] Caps typically apply to three characteristics of the mortgage: * frequency of the interest rate change * periodic change in interest rate * total change in interest rate over the life of the loan, sometimes called life cap For example, a given ARM might have the following types of caps: Interest rate adjustment caps: * interest adjustments made every 6 months, typically 1% per adjustment, 2% total per year * interest adjustments made only once a year, typically 2% maximum * interest rate may adjust no more than 1% in a year Mortgage payment adjustment caps: * maximum mortgage payment adjustments, usually 7.5% annually on pay-option/negative amortization loans Life of loan interest rate adjustment caps: * total interest rate adjustment limited to 5% or 6% for the life of the loan. Caps on the periodic change in interest rate may be broken up into one limit on the first periodic change and a separate limit on subsequent periodic change, for example 5% on the initial adjustment and 2% on subsequent adjustments. Although uncommon, a cap may limit the maximum monthly payment in absolute terms (for example, $1000 a month), rather than in relative terms. ARMs that allow negative amortization will typically have payment adjustments that occur less frequently than the interest rate adjustment. For example, the interest rate may be adjusted every month, but the payment amount only once every 12 months. Cap structure is sometimes expressed as initial adjustment cap / subsequent adjustment cap / life cap, for example 2/2/5 for a loan with a 2% cap on the initial adjustment, a 2% cap on subsequent adjustments, and a 5% cap on total interest rate adjustments. When only two values are given, this indicates that the initial change cap and periodic cap are the same. For example, a 2/2/5 cap structure may sometimes be written simply 2/5. Reasons for ARMs This section does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (July 2007) ARMs generally permit borrowers to lower their initial payments if they are willing to assume the risk of interest rate changes. In many countries, banks or similar financial institutions are the primary originators of mortgages. For banks that are funded from customer deposits, the customer deposits will typically have much shorter terms than residential mortgages. If a bank were to offer large volumes of mortgages at fixed rates but to derive most of its funding from deposits (or other short-term sources of funds), the bank would have an asset-liability mismatch: in this case, it would be running the risk that the interest income from its mortgage portfolio would be less than it needed to pay its depositors. In the United States, some argue that the savings and loan crisis was in part caused by this problem, that the savings and loans companies had short-term deposits and long-term, fixed rate mortgages, and were caught when Paul Volcker raised interest rates in the early 1980s. Therefore, banks and other financial institutions offer adjustable rate mortgages because it reduces risk and matches their sources of funding. Banking regulators pay close attention to asset-liability mismatches to avoid such problems, and place tight restrictions on the amount of long-term fixed-rate mortgages that banks may hold (in relation to their other assets). To reduce this risk, many mortgage originators will sell many of their mortgages, particularly the mortgages with fixed rates. For the borrower, adjustable rate mortgages may be less expensive, but at the price of bearing higher risk. Many ARMs have “teaser periods,” which are relatively short initial fixed-rate periods (typically one month to one year) when the ARM bears an interest rate that is substantially below the “fully indexed” rate. The teaser period may induce some borrowers to view an ARM as more of a bargain than it really represents. A low teaser rate predisposes an ARM to sustain above-average payment increases. ARM Variants Hybrid ARMs A hybrid ARM features an interest rate that is fixed for an initial period of time, then floats thereafter. The “hybrid” refers to the ARM’s blend of fixed-rate and adjustable-rate characteristics. Hybrid ARMs are referred to by their initial fixed-rate and adjustable-rate periods, for example, 3/1, is for an ARM with a 3-year fixed interest-rate period and subsequent 1-year interest-rate adjustment periods. The date that a hybrid ARM shifts from a fixed-rate payment schedule to an adjusting payment schedule is known as the reset date. After the reset date, a hybrid ARM floats at a margin over a specified index just like any ordinary ARM.[3] The popularity of hybrid ARMs has significantly increased in recent years. In 1998, the percentage of hybrids relative to 30-year fixed-rate mortgages was less than 2%; within 6 years, this increased to 27.5%.[3] Like other ARMs, hybrid ARMs transfer some interest-rate risk from the lender to the borrower, thus allowing the lender to offer a lower note rate in many interest-rate environments. Option ARMs An “option ARM” is typically a 30-year ARM that initially offers the borrower four monthly payment options: a specified minimum payment, an interest-only payment, a 15-year fully amortizing payment, and a 30-year fully amortizing payment.[4] These types of loans are also called “pick-a-payment” or “pay-option” ARMs. When a borrower makes a Pay-Option ARM payment that is less than the accruing interest, there is “negative amortization”, which means that the unpaid portion of the accruing interest is added to the outstanding principal balance. For example, if the borrower makes a minimum payment of$1,000 and the ARM has accrued monthly interest in arrears of $1,500,$500 will be added to the borrower’s loan balance. Moreover, the next month’s interest-only payment will be calculated using the new, higher principal balance. Option ARMs are often offered with a very low teaser rate (often as low as 1%) which translates into very low minimum payments for the first year of the ARM. During boom times, lenders often underwrite borrowers based on mortgage payments that are below the fully amortizing payment level. This enables borrowers to qualify for a much larger loan (i.e., take on more debt) than would otherwise be possible. When evaluating an Option ARM, prudent borrowers will not focus on the teaser rate or initial payment level, but will consider the characteristics of the index, the size of the “mortgage margin” that is added to the index value, and the other terms of the ARM. Specifically, they need to consider the possibilities that (1) long-term interest rates go up; (2) their home may not appreciate or may even lose value or even (3) that both risks may materialize. Option ARMs are best suited to sophisticated borrowers with growing incomes, particularly if their incomes fluctuate seasonally and they need the payment flexibility that such an ARM may provide. Sophisticated borrowers will carefully manage the level of negative amortization that they allow to accrue. In this way, a borrower can control the main risk of an Option ARM, which is “payment shock”, when the negative amortization and other features of this product can trigger substantial payment increases in short periods of time.[5] The minimum payment on an Option ARM can jump dramatically if its unpaid principal balance hits the maximum limit on negative amortization (typically 110% to 125% of the original loan amount). If that happens, the next minimum monthly payment will be at a level that would fully amortize the ARM over its remaining term. In addition, Option ARMs typically have automatic “recast” dates (often every fifth year) when the payment is adjusted to get the ARM back on pace to amortize the ARM in full over its remaining term. For example, a $200,000 ARM with a 110% “neg am” cap will typically adjust to a fully amortizing payment, based on the current fully-indexed interest rate and the remaining term of the loan, if negative amortization causes the loan balance to exceed$220,000. For a 125% recast, this will happen if the loan balance reaches $250,000. Any loan that is allowed to generate negative amortization means that the borrower is reducing his equity in his home, which increases the chance that he won’t be able to sell it for enough to repay the loan. Declining property values would exacerbate this risk. Option ARMs may also be available as “hybrids,” with longer fixed-rate periods. These products would not be likely to have low teaser rates. As a result, such ARMs mitigate the possibility of negative amortization, and would likely not appeal to borrowers seeking an “affordability” product. Cash flow ARMs A cash flow ARM is a minimum payment option mortgage loan. This is a fancy term for a loan that allows a borrower to choose their monthly payment from several options. These payment options usually include the option to pay at the 30-year level, 15-year level, interest only level, and a minimum payment level. The minimum payment level is usually lower than the interest only payment. This type of loan can result in negative amortization. The option to make a minimum payment is usually available only for the first several years of the loan. Cash flow ARM mortgages are synonymous with option ARM or payment option ARM mortgages, however it should be noted that not all loans with cash flow options are adjustable. In fact, fixed rate cash flow option loans retain the same cash flow options as cash flow ARMs and option ARMs, but remain fixed for up to 30 years. Loan caps Loan caps provide payment protection against payment shock, and allow a measure of interest rate certainty to those who gamble with initial fixed rates on ARM loans. There are three types of Caps on a typical First Lien Adjustable Rate Mortgage or First Lien Hybrid Adjustable Rate Mortgage. Initial Adjustment Rate Cap: The majority of loans have a higher cap for initial adjustments that’s indexed to the initial fixed period. In other words, the longer the initial fixed term, the more the bank would like to potentially adjust your loan. Typically, this cap is 2-3% above the Start Rate on a loan with an initial fixed rate term of 3 years or lower and 5-6% above the Start Rate on a loan with an initial fixed rate term of 5 years or greater. Rate Adjustment Cap: This is the maximum amount by which an Adjustable Rate Mortgage may increase on each successive adjustment. Similar to the initial cap, this cap is usually 1% above the Start Rate for loans with an initial fixed term of 3 years or greater and usually 2% above the Start Rate for loans that have an initial fixed term of 5 years or greater Lifetime Cap: Most First Mortgage loans have a 5% or 6% Life Cap above the Start Rate (this ultimately varies by the lender and credit grade). * Industry Shorthand for ARM Caps Inside the business caps are expressed most often by simply the 3 numbers involved that signify each cap. For example, a 5/1 Hybrid ARM may have a cap structure of 5/2/5 (5% initial cap, 2% adjustment cap and 5% lifetime cap) and insiders would call this a 5-2-5 cap. Alternately, a 1-year ARM might have a 1/1/6 cap (1% initial cap, 1% adjustment cap and 6% lifetime cap) known as a 1-1-6, or alternately expressed as a 1/6 cap (leaving out one digit signifies that the initial and adjustment caps are identical). * Negative amortization ARM caps See the complete article for the type of ARM that Negative amortization loans are by nature. Higher risk products, such as First Lien Monthly Adjustable loans with Negative amortization and Home Equity Lines of Credit aka HELOC have different ways of structuring the Cap than a typical First Lien Mortgage. The typical First Lien Monthly Adjustable loans with Negative amortization loan has a life cap for the underlying rate (aka “Fully Indexed Rate”) between 9.95% and 12% (maximum assessed interest rate). Some of these loans can have much higher rate ceilings. The fully indexed rate is always listed on the statement, but borrowers are shielded from the full effect of rate increases by the minimum payment, until the loan is recast, which is when principal and interest payments are due that will fully amortize the loan at the fully indexed rate. * Home Equity Lines of Credit HELOC Since HELOCs are intended by banks to primarily sit in second lien position, they normally are only capped by the maximum interest rate allowed by law in the state wherein they are issued. For example, Florida currently has an 18% cap on interest rate charges. These loans are risky in the sense that to lenders, they are practically a credit card issued to the borrower, with minimal security in the event of default. They are risky to the borrower in the sense that they are mostly indexed to the Wall Street Journal Prime Rate, which is considered a Spot Index, or a financial indicator that is subject to immediate change (as are the loans based upon the Prime Rate). The risk to borrower being that a financial situation causing the Federal Reserve to raise rates dramatically (see 1980, 2006) would effect an immediate rise in obligation to the borrower, up to the capped rate. Popularity Variable rate mortgages are the most common form of loan for house purchase in the United Kingdom, Ireland and Canada but are unpopular in some other countries. Variable rate mortgages are very common in Australia and New Zealand. In some countries, true fixed-rate mortgages are not available except for shorter-term loans; in Canada, the longest term for which a mortgage rate can be fixed is typically no more than ten years, while mortgage maturities are commonly 25 years. In many countries, it is not feasible for banks to borrow at fixed rates for very long terms; in these cases, the only feasible type of mortgage for banks to offer may be adjustable rate mortgages (barring some form of government intervention). For those who plan to move within a relatively short period of time (three to seven years), they are attractive because they often include a lower, fixed rate of interest for the first three, five, or seven years of the loan, after which the interest rate fluctuates. Pricing Adjustable rate mortgages are typically, but not always, less expensive than fixed-rate mortgages. Due to the inherent interest rate risk, long-term fixed rates will tend to be higher than short-term rates (which are the basis for variable-rate loans and mortgages). The difference in interest rates between short and long-term loans is known as the yield curve, which generally slopes upward (longer terms are more expensive). The opposite circumstance is known as an inverted yield curve and is relatively infrequent. The fact that an adjustable rate mortgage has a lower starting interest rate does not indicate what the future cost of borrowing will be (when rates change). If rates rise, the cost will be higher; if rates go down, the rate will be lower. In effect, the borrower has agreed to take the interest rate risk. Some studies have shown that on average, the majority of borrowers with adjustable rate mortgages save money in the long term.[6] The actual pricing and rate analysis of adjustable rate mortgage in the finance industry is done through various computer simulation methodologies like Monte Carlo method or Sobol sequences. In these techniques, by using an assumed probability distribution of future interest rates, numerous (10,000 – 100,000 or even 1,000,000) possible interest rate scenarios are explored, mortgage cash flows calculated under each, and aggregate parameters like fair value and effective interest rate over the life of the mortgage are estimated. Having these at hand, lending analysts determine whether offering a particular mortgage would be profitable, and if it would represent tolerable risk to the bank. Prepayment Adjustable rate mortgages, like other types of mortgage, usually allow the borrower to prepay principal (or capital) early without penalty. Early payments of part of the principal will reduce the total cost of the loan (total interest paid), but will not shorten the amount of time needed to pay off the loan like other loan types. Upon each recasting, the new fully indexed interest rate is applied to the remaining principal to end within the remaining term schedule. If a mortgage is refinanced, the borrower simultaneously takes out a new mortgage and pays off the old mortgage; the latter counts as a prepayment. Some ARMs charge prepayment penalties of several thousand dollars if the borrower refinances the loan or pays it off early, especially within the first 3 or 5 years of the loan.[1] Criticism Adjustable rate mortgages are sometimes sold to consumers who are unlikely to be able to repay the loan should interest rates rise.[7] In the United States, extreme cases are characterized by the Consumer Federation of America as predatory loans. Protections against interest rate rises include (a) a possible initial period with a fixed rate (which gives the borrower a chance to increase his/her annual earnings before payments rise); (b) a maximum (cap) that interest rates can rise in any year (if there is a cap, it must be specified in the loan document); and (c) a maximum (cap) that interest rates can rise over the life of the mortgage loan. 5. See your lender first. Find out what you can afford before you look at houses. 6. Shop around. Compare the different types of mortgages and the interest rates offered by different lenders. Have the lender validate your calculations and agree that you are qualified for a home loan and monthly payments of that size. Get prequalified. 7. Understand the deal. Ask about closing costs and other fees before you sign the documents. Ask if you will incur costs if you refinance or prepay your mortgage. 8. Work interactively with a mortgage lender. Your lender will likely need to talk with you from time to time and may need additional information. Make sure you get back to your lender quickly so the process can be completed as soon as possible. About Your Home 9. Avoid emotional buying. Before you look at any house, determine what features you really need in a home and then try to stick to the list you made. 10. Visit as many homes as possible.415-796-0086 | Hector Aldana licensed real estate broker agent • [/tab] [tab title=”FIXED MORTGAGE LOANS”]Fixed loans A fixed rate mortgage (FRM) is a mortgage loan first developed by the Federal Housing Administration (FHA)[1] where the interest rate on the note remains the same through the term of the loan, as opposed to loans where the interest rate may adjust or “float.” Other forms of mortgage loan include interest only mortgage, graduated payment mortgage, variable rate (including adjustable rate mortgages and tracker mortgages) , negative amortization mortgage, and balloon payment mortgage. Please note that each of the loan types above except for a straight adjustable rate mortgage can have a period of the loan for which a fixed rate may apply. A Balloon Payment mortgage, for example, can have a fixed rate for the term of the loan followed by the ending balloon payment. Terminology may differ from country to country: loans for which the rate is fixed for less than the life of the loan may be called hybrid adjustable rate mortgages (in the United States). This payment amount is independent of the additional costs on a home sometimes handled in escrow, such as property taxes and property insurance. Consequently, payments made by the borrower may change over time with the changing escrow amount, but the payments handling the principal and interest on the loan will remain the same. Fixed rate mortgages are characterized by their interest rate (including compounding frequency, amount of loan, and term of the mortgage). With these three values, the calculation of the monthly payment can then be done. Monthly payment formula * Note: Fixed rate mortgage interest may be compounded differently in other countries, such as in Canada, where it is compounded every 6 months. The fixed monthly payment for a fixed rate mortgage is the amount paid by the borrower every month that ensures that the loan is paid off in full with interest at the end of its term. This monthly payment c depends upon the monthly interest rate r (expressed as a fraction, not a percentage, i.e., divide the quoted yearly nominal percentage rate by 100 and by 12 to obtain the monthly interest rate), the number of monthly payments N called the loan’s term, and the amount borrowed P0 known as the loan’s principal; rearranging the formula for the present value of an ordinary annuity we get the formula for c: c = {r\over{1-(1+r)^{-N}}}P_0 For example, for a home loan for$200,000 with a fixed yearly nominal interest rate of 6.5% for 30 years, the principal is P0 = 200000, the monthly interest rate is r = 6.5 / 100 / 12, the number of monthly payments is N = 30 * 12 = 360, the fixed monthly payment c = \$1264.14. This formula is provided using the financial function PMT in a spreadsheet such as Excel. In the example, the monthly payment is obtained by entering either of the these formulas: =PMT(6.5/100/12,30*12,200000) =((6.5/100/12)/(1-(1+6.5/100/12)^(-30*12)))*200000 = 1264.14 This monthly payment formula is easy to derive, and the derivation illustrates how fixed-rate mortgage loans work. The amount owed on the loan at the end of every month equals the amount owed from the previous month, plus the interest on this amount, minus the fixed amount paid every month. Amount owed at month 0: P0 Amount owed at month 1: P1 = P0 + P0 * r − c ( principal + interest – payment)
• P1 = P0(1 + r) − c (equation 1) Amount owed at month 2: P2 = P1(1 + r) − c Using equation 1 for P1 P2 = (P0(1 + r) − c)(1 + r) − c
• P2 = P0(1 + r)2 − c(1 + r) − c (equation 2) Amount owed at month 3:
• P3 = P2(1 + r) − c Using equation 2 for P2
• P3 = (P0(1 + r)2 − c(1 + r) − c)(1 + r) − c P3 = P0(1 + r)3 − c(1 + r)2 − c(1 + r) − c Amount owed at month N: PN = PN − 1(1 + r) − c
• PN = P0(1 + r)N − c(1 + r)N − 1 − c(1 + r)N − 2…. − c PN = P0(1 + r)N − c((1 + r)N − 1 + (1 + r)N − 2…. + 1)
• PN = P0(1 + r)N − c(S) (equation 3) Where S = (1 + r)N − 1 + (1 + r)N − 2…. + 1 (equation 4) (see geometric progression) S(1 + r) = (1 + r)N + (1 + r)N − 1…. + (1 + r) (equation 5) With the exception of two terms the S and S(1 + r) series are the same so when you subtract all but two terms cancel: Using equation 4 and 5 S(1 + r) − S = (1 + r)N − 1 S((1 + r) − 1) = (1 + r)N − 1 S(r) = (1 + r)N − 1 S = {{(1+r)^N – 1}\over r} (equation 6) Putting equation 6 back into 3: P_N = P_0(1+r)^N – c {{(1+r)^N – 1}\over r} PN will be zero because we have paid the loan off. 0 = P_0(1+r)^N – c {{(1+r)^N – 1}\over r}
• We want to know c c = {{r(1+r)^N} \over {(1+r)^N-1}} P_0 Divide top and bottom with (1 + r)N c = {r \over {1-(1+r)^{-N}}} P_0

baytech mortgage commercial san francisco residential & commercial loans

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