Having trouble with APR calculation
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 Check your calculation of A**. I was able to duplicate their calculations using excel. Make you sure have accounted for all the terms, it can be easy to be one off. They are making a guess at the interest rate which will be wrong, then they are adjusting it to see how wrong it is, then making another adjustment. They will repeat until they see no movement in the guesses.
Having just purchased an upcoming Samsung phone using their 0% interest I can tell you that the justification is to give you credit. I have the same with Best Buy which is 0% for a specific initial purchase. The bank (in the Samsung case is TD Bank) establishes a rotating credit line for you. The APR after is well established at the very high side of 29.99%. Nobody in their right mind should want to pay that much interest on any purchase. My last car purchase was below 3% APR. Additionally the introductory rate will still calculate their 29.99% interest as if it existed since the first day of credit and will be applied to your balance should you ever be late on any single payment. At that time the interest is factored in as if it were always there and payments are adjusted accordingly. You see, the bank wants you to pay their high interest rate. So they entice you with the 0% and hope you either finance more on that credit line (exempt from the promotional rate) or miss a payment and they can hit you with a whammy. Specifically the question asks how this offer benefits Samsung. To answer that portion; it ensures a sale at full retail price of the phone. Samsung is just an agent between you and the bank. The bank takes on the risk for a potential high reward. There are a few things you should keep in mind when getting another vehicle: DON'T use dealership financing. Get an idea of the price range you're looking for, and go to your local bank or find a local credit union and get a pre-approval for a loan amount (that will also let you know what kind of interest rates you'll get). Your credit score is high enough that you shouldn't have any problems securing a decent APR. Check your financing institution's rules on financing beyond the vehicle's value. The CU that refinanced my car noted that between 100% and 120% of the vehicle's value means an additional 2% APR for the life of the loan. Value between 120% and 130% incurred an additional 3% APR. Your goal here is to have the total amount of the loan less than or equal to the value of the car through the sale / trade-in of your current vehicle, and paying off whatever's left out of pocket (either as a down-payment, or simply paying off the existing loan).  If you can't manage that, then you're looking at immediately being upside-down on the new vehicle, with a potential APR penalty. There are a few ways to look at this question. Assumptions. Per the original post's assumptions, this answer: In other words, if the owner paid the mortgage on its original schedule, the deal could boil down to a $ 40,000 up-front payment, in exchange for $ 200,000 of equity after 30 years.  Or the deal could boil down to a $ 40,000 up-front payment, in exchange for a $ 810.70 monthly payment starting in 30 years. While the owner is paying down the mortgage, the return on equity is the principal payment divided by the equity.  The principal payment is the net rent minus non-financing costs and interest, so it is actually a profit. The initial return on equity is 6.321 % APR, or 6.507 % APY.  This is calculated by dividing the $ 210.70 monthly principal payment by the initial $ 40,000 equity, and converting from monthly return to annual return. After 30 years, the return on equity is 4.864 % APR, or 4.974 % APY.  This is calculated by dividing the $ 810.70 monthly cash flow (which is no longer reduced by mortgage payments) by the $ 200,000 equity after 30 years, and converting from monthly return to annual return. The cap rate is the same as the return on equity in the absence of debt.  In this example, 4.864 % APR, or 4.974 % APY. The return on equity declines from 6.507 % APY initially to 4.974 % APY after 30 years. This is because the cap rate exceeds the note rate (4.974 % APY vs. 4.594 % APY), and the leverage decreases from 5x to 1x. The weighted average compound annual growth rate of the equity during the 30 years is 5.511 % APY.  Per the original poster's answer, this is computed by taking the 30th root of the 5-fold increase in equity.  Because the owner made no extra principal payments (besides those already discussed), the relevant amounts are the initial $ 40,000 owner payment and the final $ 200,000 owner equity.  5.511 % APY corresponds to a 5.377 % APR. The internal rate of return if the owner never sells can be computed by treating the deal as a $ 40,000 up-front payment, in exchange for an $ 810.70 monthly payment starting in 30 years.  The internal rate of return (IRR) is not a very useful number, because it assumes that you can somehow reinvest the eventual dividends at the same rate.  In this example, the IRR is 5.172 % APR, or 5.296  % APY.  In this example, the IRR is calculated by (iteratively) finding an interest rate for which (initial investment) * (1 + IRR) ^ (number periods before dividends start) = (periodic dividend) / (IRR - growth rate of dividend).  For example: $ 40,000 * (1.004309687)^360 = $ 810.70 / (0.004309687 - 0) = $ 188,111 I then converted the 0.431 % monthly IRR to an annual IRR. The deal can be thought of as a return on equity, plus a return on paying down the mortgage. When computing the return from paying down the mortgage, the initial equity is irrelevant.  It does not matter whether you start with a $ 160,000 mortgage on a $ 160,000 property, a $ 160,000 mortgage on a $ 200,000 property, or a $ 160,000 mortgage on a $ 1,000,000 property.  All that matters is the note rate on the mortgage, which is the applicable compound interest rate. The return on paying down the mortgage equals the note rate of the mortgage.  For a 4.5% note rate, this works out to a 4.594% annual percentage yield (APY). You can confirm this by looking at your amortization schedule.  Suppose you have a $ 160,000 mortgage with a fixed 4.5% APR note rate for 360 months.  Your monthly payment is $ 810.70.  In the first month, $ 600 goes toward interest, and $ 210.70 reduces the principal.  In other words, the $ 210.70 principal payment eliminated the need for a $ 810.70 payment 30 years later.  Notice that: . $ 210.70 * (1 + 0.045 / 12)^360 = $ 210.70 * (1.00375)^360 = $ 210.70 * 3.8477 = $ 810.71 which is within rounding error of $ 810.70. The interest rate is 3/8 % per month, which is an APR of 4.5%, and an APY of 4.594 %. "Yes it is possible, the Google Summer of Code students have been doing so for years. They get a Prepaid card and then can spend that in there local countries. They have the billing address as Google and the shipping address as their own. A few retailers have trouble but that just their systems. The trouble people have had is more in transferring the money to their personal accounts, usually there is a charge on this transfer. Transfer money from US (""prepaid"") VISA Debit to AU bank account" The MWRR that you showed in your post is calculated incorrectly. The formula that you use... ($15,750 - $15,000 - $4,000) / ($15,000 + 0.5 x $4,000) Translates into a form of the DIETZ formula of (EMV-BMV-C)/(BMV + .5 x C) The BMV is the STARTING balance. And as a matter of fact, the starting balance was NOT 15,000. It was IN FACT 11,000. See, the starting value for a month MUST BE the ending value of the prior month. So the BMV of 11,000 would give you the correct answer. Because if you added 4,000 at the start of the month (on day 1), it would have to have been ADDED to the 11,000 of the PRIOR month's ENDING value. Make sense? That would also mean that the addition of 4000 to the 11000 would imply that you started day 1 with 11,000. Make sense? Summary: When doing the calculations, you may use the ending value on the last day of the month to get your EMV. BUT YOU MAY NOT take the ending value on day 1 to get the BMV. That simply can not make sense since you already added a bunch of money during the day. Think about it. Davie Thanks for this, great in depth answer. I had previously calculated a WACC and have used it for my discount rate.   As part of your last point on revenue vs. cash, I've set a accounts receivable period of 30 days, and then applied a factor of 30/365 * revenue to understand what portion of my revenue is not cash in hand. Does that make sense? "Trying to figure out how much money you have available each day sounds like you're making this more complicated than it needs to be. Unless you're extremely tight and you're trying to squeeze by day by day, asking ""do I have enough cash to buy food for today?"" and so on, you're doing too much work. Here's what I do. I make a list of all my bills. Some are a fixed amount every month, like the mortgage and insurance premiums. Others are variable, like electric and heating bills, but still pretty predictable.  Most bills are monthly, but I have a few that come less frequently, like water bills in my area come every 3 months and I have to pay property taxes twice a year. For these you have to calculate how much they cost each month. Like for the water bill, it's once every 3 months so I divide a typical bill by 3. Always round up or estimate a little high to be safe. Groceries are a little tricky because I don't buy groceries on any regular schedule, and sometimes I buy a whole bunch at once and other times just a few things. When groceries were a bigger share of my income, I kept track of what I spent for a couple of months to figure out an average per month. (Today I'm a little richer and I just think of groceries as coming from my spending money.) I allocate a percentage of my income for contributions to church and charities and count this just like bills. It's a good idea to put aside something for savings and/or paying down any outstanding loans every month. Then I add these up to say okay, here's how much I need each month to pay the bills. Subtract that from my monthly income and that's what I have for spending money. I get paid twice a month so I generally pay bills when I get paid. For most bills the due date is far enough ahead that I can wait the maximum half a month to pay it. (Worst case the bill comes the day after I pay the bills from this paycheck.)  Then I keep enough money in my checking account to, (a) Cover any bills until the next paycheck and allow for the particularly large bills; and (b) provide some cushion in case I make a mistake -- forget to record a check or make an arithmetic error or whatever; and (c) provide some cushion for short-term unexpected expenses. To be safe, (a) should be the total of your bills for a month, or as close to that as you can manage. (b) should be a couple of hundred dollars if you can manage it, more if you make a lot of mistakes. If you've calculated your expenses properly and only spend the difference, keeping enough money in the bank should fall out naturally. I think it's a lot easier to try to manage your money on a monthly basis than on a daily basis. Most of us don't spend money every day, and we spend wildly different amounts from day to day. Most days I probably spend zero, but then one day I'll buy a new TV or computer and spend hundreds.  Update in response to question What I do in real life is this: To calculate my available cash to spend, I simply take the balance in my checking account -- assuming that all checks and electronic payments have cleared. My mortgage is deducted from my checking every month so I post that to my checking a month in advance. I pay a lot of things with automatic charges to a credit card these days, so my credit card bills are large and can't be ignored. So subtract my credit card balances. Subtract my reserve amount. What's left is how much I can afford to spend. So for example: Say I look at the balance in my checkbook today and it's, say, $3000. That's the balance after any checks and other transactions have cleared, and after subtracting my next mortgage payment. Then I subtract what I owe on credit cards. Let's say that was $1,200. So that leaves $1,800. I try to keep a reserve of $1,500. That's plenty to pay my routine monthly bills and leave a healthy reserve. So subtract another $1,500 leaves $300. That's how much I can spend. I could keep track of this with a spreadsheet or a database but what would that gain? The amount in my checking account is actual money. Any spreadsheet could accumulate errors and get farther and farther from accurate values. I use a spreadsheet to figure out how much spending money I should have each month, but that's just to use as a guideline. If it came to, say, $100, I wouldn't make grandiose plans about buying a new Mercedes. If it came to $5,000 a month than buying a fancy new car might be realistic. It also tells me how much I can spend without having to carefully check balances and add it up. These days I have a fair amount of spending money so when, for example, I recently decided I wanted to buy some software that cost $100 I just bought it with barely a second thought. When my spending money was more like $100 a month, lunch at a fast food place was a big event that I planned weeks in advance. (Obviously, I hope, don't get stupid about ""small amounts"". If you can easily afford $100 for an impulse purchase, that doesn't mean that you can afford $100 five times a day every day.) Two caveats: 1. It helps to have a limited number of credit cards so you can keep the balances under control. I have two credit cards I use for almost everything, so I only have two balances to keep track of. I used to have more and it got confusing, it was easy to lose track of how much I really owed, which is a set up for getting in trouble." If I understand you right, what you need is the minimum amount in the account until your next deposit.  So for example, if today is the 10th and you get paid on the 15th, how much do I need to have in the account, so I know how much I can spend?  That amount should be all of the bills that will be paid between today and the 15th. An alternative would just to keep a running balance and see what the minimum value is. My personal finance software does that for me, but it's possible, although a little more complicated, in Excel.  You'd have to find the date of the next deposit, and do a SUMIF looking for dates between today and that date.  That's about as far as I can get without getting off-topic.