vania-janet/multiturn-rag-retrieval-data huggingface dataset:
What is the formula for calculating the total cost of a loan with extra payments towards the principal? The formula you require is the standard one for calculating the time to repay.  With larger repayments the time to completely repay the loan is reduced. Where The total cost of the loan is then n * d. Explanation & Calculation The formula for a loan is derived from the sum of the cash flows discounted to present value being equal to the principal.  For further info see the section here titled: Calculating the Present Value of an Ordinary Annuity The summation can be reduced to a closed form by induction:  Rearranging for d and n With the OP's figures The original monthly repayment is $1,006.96 Adding $200 each month ... With the higher repayment the loan is repaid in 257.36 months instead of 360.  (Of course a bank would simply take a reduced payment in month 258, but the amounts work out the same.) The saving is $51,882.37 Addendum If the repayments increase was made part-way through the term of the loan the summation and formula would be  Where Then For example, if for the first ten years the payments are $1,006.96 and for the remaining time the repayments are $1,206.96 The loan is completely repaid in 302.528 months. The saving is Plotting over a range of m months:
Illustrating with a shorter example:  Suppose I deposit 1,000 USD. Every year I deposit another 100 USD. I want to know how much money will be on that savings account in 4 years.  The long-hand calculation is Expressed with a summation  And using the formula derived from the summation (as shown by DJohnM) So for 20 years Note in year 20 (or year 4 in the shorter example) the final $100 deposit does not have any time to accrue interest before the valuation of the account.
"I'm not an expert, but here is my best hypothesis. On Microsoft's (and most other company's) cash flow statements, they use the so-called ""indirect method"" of accounting for cash flow from operations. How that works, is they start with net income at the top, and then adjust it with line items for the various non-cash activities that contributed to net income. The key phrase is that these are accounting for the non-cash activities that contribute to net income. If the accounts receivable amount changes from something other than operating activity (e.g., if they have to write off some receivables because they won't be paid), the change didn't contribute to net income in the first place, so doesn't need to be reconciled on the cash flow statement."
The key to understanding a mortgage is to look at an amortization schedule.  Put in 100k, 4.5% interest, 30 years, 360 monthly payments and look at the results.  You should get roughly 507 monthly P&I payment.  Amortization is only the loan portion, escrow for taxes and insurance and additional payments for PMI are extra. You'll get a list of all the payments to match the numbers you enter.  These won't exactly match what you really get in a mortgage, but they're close enough to demonstrate the way amortization works, and to plan a budget.  For those terms, with equal monthly payments, you'll start paying 74% interest from the first payment.  Each payment thereafter, that percentage drops. The way this is all calculated is through the time value of money equations.  https://en.wikipedia.org/wiki/Time_value_of_money.  Read slowly, understand how the equations work, then look at the formula for Repeating Payment and Present Value.  That is used to find the monthly payment.   You can validate that the formula works by using their answer and making a spreadsheet that has these columns:  Previous balance, payment, interest, new balance.  Each line represents a month.  Calculate interest as previous balance * APR/12.  Calculate new balance as previous balance minus payment plus interest. Work through all this for a 1 year loan and you will understand a lot better.
&gt;I don't understand the logic of converting a cost of funds of 4% to a monthly % and then subtracting that number from an annual one (the 1.5%).  I know it was wrong, so how would you approach it?  &gt;Unfortunately without seeing the case I really can't help you...there was likely much you have left out from above.    All the relevant details I received for the case are here. What other info are you looking for?
"In Orange County (southern California), one agent has blogged pretty extensively about using rental parity to determine when it is time to rent or buy. Rental parity is achieved when the cost of renting is equal to the cost of owning; in theory, if you buy when a home is selling above rental parity, you're overpaying, and you'd be better off renting. He has many posts on the subject; a few you might care to read would be this one, and this other one. You might get a better sense of how to calculate rental parity by looking at an example or two. There is also the NY Times calculator mentioned in other responses, and the Patrick.net calculator. Be aware, the calculators are garbage in, garbage out. In other words, you have to consider the input carefully. In particular, I found the defaults on the Patrick.net calculator were not realistic. So far as I am aware, the agent at OCHousingNews does not make his calculations public (though I have never actually asked). He's using a spreadsheet which I have never seen. That is another option, if you care to do this kind of analysis yourself. Search around, you can find a spreadsheet that someone has posted here and there. But keeping something like that updated is not trivial. In my experience, in practice, it's difficult to be totally rational and mathematical when it comes to many decisions, and as other respondents have noted, where you live is one of those decisions. Too, saying ""buy when rental parity is achieved"" is sort of like saying ""buy low, sell high,"" as though it were perfectly clear when stocks are at a bottom and/or a peak. In our case, we bought a house about 12 years ago, before rental parity was being discussed in the blogsphere. Looking back, we supposedly bought at the wrong time, according to that agent's rating system, but it turned out fine for us. Our house has appreciated, whereas the S&P 500 is basically where it was 12 years ago. Had we been thinking in terms of rental parity, we might not have bought at that time.
Points are index based.  Simple take the total value of the stocks that compose the index, and set it equal to an arbitrary number. (Say 100 or 1000)  This becomes your base.  Each day, you recalculate the value of the index basket, and relate it to the base.  So if our index on day 0 was 100, and the value of the basket went up 1%, the new index would be 101 points. For the example given, the percentage change would be (133.32 -133.68  ) / 133.68 * 100% = -0.27%  Keep in mind that an index basket will change in composition over time.  Assets are added and removed as the composition of the market changes.  For example, the TSX index no longer includes Nortel, a stock that at one time made up a significant portion of the index.  I'm not sure if a percentage drop in an index is really a meaningful statistic because of that.   It is however, a good way of looking at an individual instrument.
The number you are trying to calculate is called the Internal Rate of Return (IRR).  Google Spreadsheets (and excel) both have an XIRR function that can do this for you fairly simply. Setup a spreadsheet with 1 column for dates, 1 column for investment. Mark your investments as negative numbers (payment to invest).  All investments will be negative. Mark your last row with today's date and today's valuation (positive). All withdrawals will be positive, so you are pretending to withdrawal your entire account for the purpose of calculation. Do not record dividends or other interim returns unless you are actually withdrawing money. The XIRR function will calculate your internal rate of return with irregularly timed investments. Links: Article explaining XIRR function (sample spreadsheet in google docs to modify)
So if someone would invest 14000 credits on 1st April 2016, he'd get monthly dividend = ((14000 ÷ 14) × 0.0451) × (1 - 1.42 ÷ 100) = 44.459 credits, right? One would get ((14000 ÷ 14) × 0.0451) = 45.1 is what you would get. The expenses are not to be factored. Generally if a scheme has less expense ratio, the yield is more. i.e. this has already got factored in 0.0451. If the expense ratio was less, this would have been 0.05 if expense ration would have been more it would have been 0.040. Can I then consider the bank deposit earning a higher income per month than the mutual fund scheme? As the MIP as classified as Hybrid funds as they invest around 30% in equities, there is no tax on the income. More so if there is a lock-in of 3 years. In Bank FD, there would be tax applicable as per tax brackets.
"I could not figure out a good way to make XIRR work since it does not support arrays.  However, I think the following should work for you: Insert a column at D and call it ""ratio"" (to be used to calculate your answer in column E).  Use the following equation for D3: =1+(C3-B3-C2)/C2 Drag that down to fill in the column. Set E3 to: =(PRODUCT(D$3:D3)-1)*365/(A3-A$2) Drag that down to fill in the column. Column E is now your annual rate of return."
Annuity calculation formulas can be found here. http://en.wikipedia.org/wiki/Annuity_(finance_theory). In addition, as suggested in the comments, there are many sites that have calculators. Having said that, a simple financial mechanism that is followed by many is to invest a portion of the fund in regular income instruments, for example Govt. or corporate bonds that pay a regular coupon/interest and some in diversified instruments like gold, stock etc. The exact proportion is dependent on may factors, like mortality, inflation, lifestyle, health care requirements, other expenses. The regular income provides the day to day expenses on a monthly/yearly basis, while the other instruments hedge against inflation and provide growth.
It sounded an interesting question, so I looked it up. The reason I asked about the tax years is because it matters. If the bonus was paid, and then returned in the same year - it should not appear on your W2 at all, and your taxes would be calculated accordingly. You might end up with overpayment of FICA taxes, but you can get that credited on your tax return. If, however, the repayment is not in the same year as the payment, it becomes more complicated. The code section that deals with it is 26 USC § 1341. What it says, in short, is this: you can deduct the repaid amount from your current taxable income, but only if its more than $3000. The tax benefit of such deduction cannot exceed the actual tax paid on this in the year when you got the bonus (i.e.: you need to calculate that year with the amount, and without the amount - the credit cannot exceed the difference). But it can also not exceed the amount you would be paying on that amount in the current year (i.e.: if current taxes are less than that year - you lost the difference). If the signing bonus is less than $3000 and it spans across tax years - you cannot deduct it. Bummer.
There are different perspectives from which to calculate the gain, but the way I think it should be done is with respect to the risk you've assumed in the original position, which the simplistic calculation doesn't factor in. There's a good explanation about calculating the return from a short sale at Investopedia.  Here's the part that I consider most relevant: [...] When calculating the return of a short sale, you need to compare the amount the trader gets to keep to the initial amount of the liability.   Had the trade in our example turned against you, you (as the short   seller) would owe not only the initial proceeds amount but also the   excess amount, and this would come out of your pocket. [...] Refer to the source link for the full explanation. Update: As you can see from the other answers and comments, it is a more complex a Q&A than it may first appear.  I subsequently found this interesting paper which discusses the difficulty of rate of return with respect to short sales and other atypical trades: Excerpt: [...]   The problem causing this almost uniform omission of a percentage   return on short sales, options (especially writing), and futures, it   may be speculated, is that the nigh-well universal and conventional   definition of rate of return involving an initial cash outflow   followed by a later cash inflow does not appear to fit these   investment situations. None of the investment finance texts nor   general finance texts, undergraduate or graduate, have formally or   explicitly shown how to resolve this predicament or how to justify the   calculations they actually use. [...]
It depends on the country and possibly the bank. In the United States, my savings accounts compound monthly, using the average balance for the month. You should have an account agreement or terms document that details how the bank does computations like interest payments.
"When we talk about compounding, we usually think about interest payments. If you have a deposit in a savings account that is earning compound interest, then each time an interest payment is made to your account, your deposit gets larger, and the amount of your next interest payment is larger than the last. There are compound interest formulas that you can use to calculate your future earnings using the interest rate and the compounding interval.  However, your mutual fund is not earning interest, so you have to think of it differently. When you own a stock (and your mutual fund is simply a collection of stocks), the value of the stock (hopefully) grows. Let's say, for example, that you have $1000 invested, and the value goes up 10% the first year. The total value of your investment has increased by $100, and your total investment is worth $1100. If it grows by another 10% the following year, your investment is then $1210, having gained $110.  In this way, your investment grows in a similar way to compound interest. As your investment pays off, it causes the value of the investment to grow, allowing for even higher earnings in the future. So in that sense, it is compounding. However, because it is not earning a fixed, predictable amount of interest as a savings account would, you can't use the compound interest formula to calculate precisely how much you will have in the future, as there is no fixed compounding interval.  If you want to use the formula to estimate how much you might have in the future, you have to make an assumption on the growth of your investment, and that growth assumption will have a time period associated with it. For example, you might assume a growth rate of 10% per year. Or you might assume a growth rate of 1% per month. This is what you could use in a compound interest formula for your mutual fund investment.  By reinvesting your dividends and capital gains (and not taking them out in cash), you are maximizing your ""compounding"" by allowing those earnings to cause your investment to grow."
Utilization is near real-time. What that means is that what is reported is what is taken in terms of debt-to-income (DTI) ratios. When a mortgage broker pulls your credit, they will pull the latest balances with the minimum payments. This is what is taken to determine DTI along with your gross monthly income. If you do not pay your account in full before the statement date, then you more than likely will have to wait an additional statement cycle before it reports to the credit bureaus. Therefore, your utilization is dynamic and the history of your utilization month-to-month is not recorded forever. Only the current balance. What is maintained and reported is your payment history. So you want to never be late if you want to be approved anytime soon for a mortgage. A lower DTI will not help your interest rate. As long as you stay away from the maximum DTI for the mortgage vehicle you are attempting to be approved for (VA, FHA, Conventional, etc), then your DTI should not be a concern. If you are borderline at the time of underwriting, you can take the opportunity and pay off the balances. The mortgage company can then do what is called a credit supplement which entails contacting those lenders where you have proven you have a zero balance and manually input the zero balance cards, that have not yet reported to the bureaus, in your final application to the mortgage company for underwriting approval.
The first method is the correct one. You bought an asset worth of $1000 and you put it on your depreciation schedule. What it means is that you get to write off the $1000 over a certain period of time (and not at once, as you do with expenses). But the value you're writing off is the $1000 regardless of how much you've written off already. Assume you depreciate in straight line over 5 years (that's how you depreciate computers for Federal tax purposes, most states follow). For the simplicity of the calculation, assume you depreciate each year as a whole year (no mid-year/mid-quarter conventions). The calculation is like this: If you sell the computer - the proceeds above the adjusted basis amount are taxed as depreciation recapture up to the accumulated depreciation amount, and as capital gains above that. So in your case - book value is the adjusted basis at the end of the year (EOY), depreciation this year is the amount you depreciate in the year in question out of the total of the original cost, and the accumulated depreciation is the total depreciation including the current year. In Maryland they do not allow depreciating to $0, but rather down to 25% of the original cost, so if you bought a $1000 computer - you depreciate until your adjusted basis is $250. Depreciation rates are described here (page 5). For computers (except for large mainframes) you get 30% depreciation, with the last year probably a bit less due to the $250 adjusted basis limitation.
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."
IRR is not subjective, this is a response to @Laythesmack, to his remark that IRR is subjective. Not that I feel a need to defend my position, but rather, I'm going to explain his.  My company offered stock at a 15% discount. We would have money withheld from pay, and twice per year buy at that discount. Coworkers said it was a 15% gain. I offered some math. I started by saying that 100/85 was 17.6%, and that was in fact, the gain. But, the funds were held by the company for an average of 3 months, not 6, so that gain occurred in 3 months and I did the math 1.176^4 and resulted in 91.5% annual return. This is IRR.  It's not that it's subjective, but it assumes the funds continue to be invested fully during the time. In our case the 91.5% was real in one sense, yet no one doubled their money in just over a year.  Was the 91% useless? Not quite. It simply meant to me that coworkers who didn't participate were overlooking the fact that if they borrowed money at a reasonable rate, they'd exceed that rate, especially for the fact that credit lines are charged day to day. Even if they borrowed that money on a credit card, they'd come out ahead.  IRR is a metric. It has no emotion, no personality, no goals. It's a number we can calculate. It's up to you to use it correctly.
"The translation scheme is detailed in IRS Publication 15, ""Employer's Tax Guide"". For the 2010 version, the information is in Section 16 on Page 37. There are two ways that employers can calculate the withheld tax amount: wage bracket and percentage. Alternatively, they can also use one of the methods defined in IRS Publication 15-A. I'll assume the person making $60k/yr with 10 allowances is paid monthly ($5000/period) and married. Using the wage bracket method, the amount withheld for federal taxes would be $83 per pay period. Using the percentage method, it would be $81.23 per pay period. I don't recommend that you use this information to determine how to fill out your W-4. The IRS provides a special online calculator for that purpose, which I have always found quite accurate. Note: ""allowances"" are not the same as ""dependents""; ""allowances"" are a more realistic estimation of your tax deductions, taking into consideration much more than just your dependents."
"The best way to do this is to use IRR.  It's a complicated calculation, but will take into account multiple in/out cash flows over time along with ""idle periods"" where your money may not have been doing anything.  Excel can calculate it for you using the XIRR function"
No idea.   I dont know what rules were put in place after 2008 in regards to rating them.  IIRC the institution doesnt have the ability to choose moodys or standard and poors. The cdos are submitted to both of them and rated anonymously. But i have no idea where im getting that from.
Starting in C2, label the cells/columns as: ""Rate"", ""Car Value"", ""Loan Balance"", ""Payment"", ""Paid to Interest"", ""Principal"", and ""Accumulated Equity"". Then select and copy cells C2:I2 as the next set of column headers beginning in K2. (I usually skip a column to leave space because I'm OCD like that :) ) Numbers: Now you need to set up your initial set of numbers for each table. We'll do the older car in the left hand table and the newer one on the right. Let's say your rate is 5% APR. Put that in cell C1 (not C3). Then in cell C3 type =C$1/12. Car Value $12,000 in Cell D3. Then type ""Down Payment"" in cell E1 and put 10% in cell D1. And last, in cell E3 put the formula =D3*(1-D$1). This should leave you with a value for the first month in the Rate, Car Value, and Loan Balance columns. Now select C1:E3 and paste those to the right hand table. The only thing you will need to change is the ""Car Value"" to $20,000. As a check, you should have .0042 / 12,000 / 10,800 on the left and then .0042 / 20,000 / 18,000 on the right. Formulas again: This is where spreadsheets become amazing. If we set up the right formulas, you can copy and paste them and do this very complicated analysis very quickly. Payment The excel formula for Payment is =PMT(Rate, NPER, PV, FV). FV is usually zero. So in cell F3, type the formula =PMT(C3, 60, E3, 0). Obviously if you're really doing a 48 month (4 year) loan then you'll need to change the 60 to 48. You should be able to copy the result from cell F3 to N3 and the formula will update itself.