Calculate Finance Rate, Interest Amount when we have below line Fees
The equation for the payment is  This board does not support Latex (the number formatting code) so the above is an image, the code is M is the payment calculated, n is the number of months or periods to pay off, and i is the rate per period. You can see that with i appearing 3 times in this equation, it's not possible to isolate to the form i=....  so a calculator will 'guess,' and use, say, 10%. It then raises or lowers the rate until the result is within the calculator's tolerance. I've observed that unlike other calculations, when you hit the button to calculate, a noticeable time lag occurs. I hope I haven't read too much into your question, it seemed to me this was what you asked.
Do you know how many people end up with an 18-21% rate on their credit card?  They started off with low teaser rates.  There was an article about it recently on Yahoo.  Mainly this comes from a lack of discipline, or an unforeseen emergency.  However, lets assume, that you are a bit uncommon and have iron discipline. It comes down to a math question.  What is the rate on your student loan?  I am going to assume 6%, and lets say that you are now paying interest.  So there is 7 months between now an then, you would pay $140 (4000 * .06/12 * 7) in interest if you left it on the student loan. Typically there is not really a free lunch with the zero percent interest rate CC.  They often charge a 3% balance transfer fee, so you would pay that on the entire amount, about $120.   Is it worth the $20?  I would say not.   However, those simple calculations are not really correct.  Since you would have to pay the CC $588.6/month to take care of this, you have to shrink the balance on the student loan to do a true apples to apples comparison.   So doing a little loan amortization, you can retire $4000 on the student loan only paying $583/month, and paying a total of $80.40 in interest. So it would cost you money to do what you are suggesting if there is a 3% transfer fee.   Even if there is no transfer fee, you only save about $80 in interest.   If it was me, I would direct my energy in other areas, like trying to bring in more money to make this student loan go away ASAP. Oh and GO STEELERS! &gt; But so long as the incremental improvement to your bottom line is there, the investment is sound, with or without taxes.  wat  If E(ROA)&gt;0 it's a sound investment? Not at all.  &gt; any investment the company makes that improves their net income automatically means more money for the company  Where is this money coming from? If it's debt-financed it escapes corporate tax rate because interest payments are deductible. Is it coming from the company's retained earnings? We have less of that now because we hiked up the corporate tax rate.   Your argument also neglects the impact corporate taxes have on equity financing and corporate leverage. 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% "There are some loan types where your minimum payment may be less than the interest due in the current period; this is not true of credit cards in the US.  Separately, if you have a minimum payment amount due of less than the interest due in the period, the net interest amount would just become principal anyway so differentiating it isn't meaningful. With credit cards in the US, the general minimum calculation is 1% of the principal outstanding plus all interest accrued in the period plus any fees.  Any overpayment is applied to the principal outstanding, because this is a revolving line of credit and unpaid interest or fees appear as a charge just like your coffee and also begin to accrue interest.  The issue arises if you have multiple interest rates.  Maybe you did a balance transfer at a discounted interest rate; does that balance get credited before the balance carried at the standard rate?  You'll have to call your lender.  While there is a regulation in place requiring payment to credit the highest rate balance first the banks still have latitude on how the payment is literally applied; explained below.   When there IS an amortization schedule, the issue is not ""principal or interest"" the issue is principle, or the next payment on the amortization schedule.  If the monthly payment on your car loan is $200, but you send $250, the bank will use the additional $50 to credit the next payment due.  When you get your statement next month (it's usually monthly) it will indicate an amount due of $150.  When you've prepaid more than an entire payment, the next payment is just farther in to the future.  You need to talk to your lender about ""unscheduled"" principal payments because the process will vary by lender and by specific loan. Call your lender.  You are a customer, you have a contract, they will explain this stuff to you.  There is no harm that can possibly come from learning the nuances of your agreement with them. Regarding the nuance to the payment regulation: A federal credit card reform law enacted in May 2009 requires that credit card companies must apply your entire payment, minus the required minimum payment amount, to the highest interest rate balance on your card.  Some credit card issuers are aggressive here and apply the non-interest portion of the minimum payment to the lowest interest rate first.  You'll need to call your bank and ask them." "My advice: IMO, all things being somewhat equal, you should always try to retire debts as quickly as possible in most cases, so start with the small cases. The method of calculating credit card interest is written on the statement. Usually it is ""average daily balance method"". Don't sweat the details. Just pay the things off." If your APR is quoted as nominal rate compounded monthly, the APR is 108.6 %. Here is the calculation, (done in Mathematica ). The sum of the discounted future payments (p) are set equal to the present value (pv) of the loan, and solved for the periodic interest rate (r).  Details of the effective interest rate calculation can be found here. http://en.wikipedia.org/wiki/Effective_interest_rate#Calculation This is a clear example of annuities, where you are trying to find Net Present Value (NPV). To find a quick solution you can use the excel function (=NPV). Solving it without excel is slightly more complicated. You have to use the annuities formula:  (Payment/rate) * (1 - 1/(1+r)^n )  This formula can be written in many different ways, this is one of the simplest.  So how do we translate that to your problem? For the first option: -5000/0.04 * (1 - 1/(1.04^2 ) = -9430.47 If you haven't made this years 5000 payment you have to subtract this years 5000, so option 1 would equal -14430,47.  Option 2 is similar -2000/0.04 (1 - 1/(1.04^10 ) = -16221.79 WAIT! You also have to subtract the initial cost so option 2 is -36221.79  So in essence, option 1 is better (but you will have to buy a machine sooner or later).  Part 2 (discount rate = 12%) is for you to understand the importance of high rates in long periods of time (like option 2's 10 years)    EDIT: For clearer formulas. Also made a mistake calculating option 2 The solution to this problem is somewhat like grading on a curve. Use the consumption ratio multiplied by the attendance (which is also a ratio, out of 100 days) to calculate how much each person owes. This will leave you short. Then add together all of the shares in a category, determine the % increase required to get to the actual cost of that category, and increase all the shares by that %.