APR for a Loan Paid Off Monthly
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% 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
You're looking for the amortization calculation. This calculation is essentially solving for the series of cash flows that will yield a zero balance after the specified term, at the given rate for a loan amount. Once you have solved for the payment amount, you can add additional principal amount to each payment period and see the interest payments and time to zero balance drop. There is a way to get a reasonable estimate of what you still owe, and then the way to get the exact value. When the loan started they should have given you amortization table that laid out each payment including the principal, interest and balance for each payment. If there are any other fees included in the payment those also should have been detailed. Determine how may payments you have maid: did you make the first payment on day one, or the start of the next month? Was the last payment the 24th, or the next one? The table will then tell you what you owe after your most recent payment. To get the exact value call the lender. The amount grows  between payment due to the interest that is accumulating. They will need to know when the payment will arrive so they can give you the correct value. To calculate how much you will save do the following calculation: payment = monthly payment for principal and interest paymentsmade =Number of payments made = 24 paymentsremaining = Number of payments remaining = 60 - paymentsmade = 60-24 = 36 instantpayoff = number from loan company  savings = (payment * paymentsremaining ) - instantpayoff Using the following loan equations where  and With the balance b[n] in period n given by Applying the OP's figures Check & demonstration Switching to $96 payment every 10 days, with 365.2422 days per year  Paying $96 every 10 days saves $326.85 and pays the loan down 2.68 months quicker. Just to add: the 20% APR is the annualized interest rate, but applied monthly. So you'd be charged $0.50 of interest on your $30 balance, which gets capitalized on the next month. So if you were to miss the next payment for some reason, your new interest charge would be on $30.50 instead of $30 (actually, it'd be much more since there would be a fee for the late payment, but discounting that to illustrate the point). A payment of $224 at 7.2% interest will pay off a $33000 mortgage in 30 years. Unfortunately, I'm on cold medicine so guessing was the only way I got to the answer, but I guessed right on the first try :). However, if you like algebra: The following formula is used to   calculate the fixed monthly payment   (P) required to fully amortize a loan   of L dollars over a term of n months   at a monthly interest rate of c. [If   the quoted rate is 6%, for example, c   is .06/12 or .005]. P = L[c(1 + c)n]/[(1 + c)n - 1] "So with any debt, be it a loan or a bond or anything else, you have two parts, the principal and the interest. The interest payment is calculated by applying the interest % to the principal. Most bonds are ""bullet bonds"" which means that the principle remains completely outstanding for the life of the bond and thus your interest payments are constant throughout the life of the bond (usually paid semi-annually). Typically part of the purpose of these is to be indefinitely refinanced, so you never really pay the principal back, though it is theoretically due at expiration.  What you are thinking of when you say a loan from a bank is an amortizing loan. With these you pay an increasing amount of the principal each period calculated such that your payments are all exactly the same (including the final payment).  Bonds, just like bank loans, can be bullet, partially amortizing (you pay some of the principle but still have a smaller lump sum at the end) and fully amortizing. One really common bullet structure is ""5 non-call 3,"" which means you aren't allowed to pay the principle down for the first three years even if you want to! This is to protect investors who spend time and resources investing in you!" "Loan officer here. Yes. You pay the per diem. I'd recommend not paying it off for like 6 months. You can pay it down to basically nothing and then hold it for six months and pay it off. Better for credit. If it's a simple interest rate, most car loans are, multiply the current principal balance by the interest rate and divide it by 365. That's the per diem or daily interest. For example, ""10,000 dollar auto loan at 3%. 10000*0.03= 300. 300/365= 0.82. So each day the balance is 10k the loan cost 82 cents. So in a month, your first payment is 100 dollars, 24.65 goes to interest 75.35 goes to principal. Then the new principal is 9924.65. So the next month, another 30 days with the new per diem of 0.815, the 100 payment is 75.50 in principal 24.50 in interest and so on." "What you are looking for is the ""debt maturity profile"" (to make it easier to google. Most countries continuously roll over their debt, in effect just paying interest forever. So when your debt is due, you issue another loan for the same amount and use the new loan to pay off the old one." From here The formula is M = P * ( J / (1 - (1 + J)^ -N)). M: monthly payment RESULT = 980.441... P: principal or amount of loan 63963 (71070 - 10% down * 71070) J: monthly interest; annual interest divided by 100, then divided by 12. .00275 (3.3% / 12) N: number of months of amortization, determined by length in years of loan. 72 months See this wikipedia page for the derivation of the formula Lower risk of having to fight to get their money back, obviously. That's what credit rating is supposed to predict. Paying your bills on time, and paying off the balance in full every month, are different questions. They want to know that you will make the minimum payments at least, and that you will eventually pay back the loan. Compare that with subprime and/or loan sharks, where the assumption is that being late or defaulting is more common, and interest rates are truly obscene in order to make a profit despite that. There is no interest outstanding, per se.  There is only principal outstanding.  Initially, principal outstanding is simply your initial loan amount. The first two sections discuss the math needed - just some arithmetic. The interest that you owe is typically calculated on a monthly basis.  The interested owed formula is simply (p*I)/12, where p is the principal outstanding, I is your annual interest, and you're dividing by 12 to turn annual to monthly. With a monthly payment, take out interest owed.  What you have left gets applied into lowering your principal outstanding.  If your actual monthly payment is less than the interest owed, then you have negative amortization where your principal outstanding goes up instead of down. Regardless of how the monthly payment comes about (eg prepay, underpay, no payment), you just apply these two calculations above and you're set.  The sections below will discuss these cases in differing payments in detail. For a standard 30 year fixed rate loan, the monthly payment is calculated to pay-off the entire loan in 30 years.  If you pay exactly this amount every month, your loan will be paid off, including the principal, in 30 years.  The breakdown of the initial payment will be almost all interest, as you have noticed.  Of course, there is a little bit of principal in that payment or your principal outstanding would not decrease and you would never pay off the loan. If you pay any amount less than the monthly payment, you extend the duration of your loan to longer than 30 years.  How much less than the monthly payment will determine how much longer you extend your loan.  If it's a little less, you may extend your loan to 40 years.  It's possible to extend the loan to any duration you like by paying less.  Mathematically, this makes sense, but legally, the loan department will say you're in breach of your contract. Let's pay a little less and see what happens.  If you pay exactly the interest owed = (p*I)/12, you would have an infinite duration loan where your principal outstanding would always be the same as your initial principal or the initial amount of your loan.   If you pay less than the interest owed, you will actually owe more every month.  In other words, your principal outstanding will increase every month!!!  This is called negative amortization.  Of course, this includes the case where you make zero payment.  You will owe more money every month. Of course, for most loans, you cannot pay less than the required monthly payments.  If you do, you are in default of the loan terms. If you pay more than the required monthly payment, you shorten the duration of your loan.  Your principal outstanding will be less by the amount that you overpaid the required monthly payment by.  For example, if your required monthly payment is $200 and you paid $300, $100 will go into reducing your principal outstanding (in addition to the bit in the $200 used to pay down your principal outstanding).  Of course, if you hit the lottery and overpay by the entire principal outstanding amount, then you will have paid off the entire loan in one shot! When you get to non-standard contracts, a loan can be structured to have any kind of required monthly payments.  They don't have to be fixed.   For example, there are Balloon Loans where you have small monthly payments in the beginning and large monthly payments in the last year.   Is the math any different?  Not really - you still apply the one important formula, interest owed = (p*I)/12, on a monthly basis.  Then you break down the amount you paid for the month into the interest owed you just calculated and principal.  You apply that principal amount to lowering your principal outstanding for the next month. Supposing that what you have posted is accurate, the most likely scenario is that you have a structured 5 year car loan where your monthly payments are smaller than the required fixed monthly payment for a 5 year loan, so even after 2 years, you owe as much or more than you did in the beginning!  That means you have some large balloon payments towards the end of your loan.  All of this is just part of the contract and has nothing to do with your prepay. Maybe I'm incorrect in my thinking, but I have a question about   prepaying a loan. When you take out a mortgage on a home or a car   loan, it is my understanding that for the first years of payment you   are paying mostly interest. Correct. So, let's take a mortgage loan that allows prepayment without penalty.   If I have a 30 year mortgage and I have paid it for 15 years, by the   16th year almost all the interest on the 30 year loan has been paid to   the bank and I'm only paying primarily principle for the remainder of   the loan. Incorrect.  It seems counter-intuitive, but even in year 16, about 53% of your monthly payment still goes to interest!!!  It is hard to see this unless you try to do the calculations yourself in a spreadsheet. If suddenly I come into a large sum of money and decide I want to pay   off the mortgage in the 16th year, but the bank has already received   all the interest computed for 30 years, shouldn't the bank recompute   the interest for 16 years and then recalculate what's actually owed in   effect on a 16 year loan not a 30 year loan? It is my understanding   that the bank doesn't do this. What they do is just tell you the   balance owed under the 30 year agreement and that's your payoff   amount. Your last sentence is correct.  The payoff amount is simply the principal outstanding plus any interest from (p*I)/12 that you owe.  In your example of trying to payoff the rest of your 30 year loan in year 16, you will owe around 68% of your original loan amount. That seems unfair. Shouldn't the loan be recalculated as a 16 year   loan, which it actually has become? In fact, you do have the equivalent of a 15 year loan (30-15=15) at about 68% of your initial loan amount.  If you refinanced, that's exactly what you would see.  In other words, for a 30y loan at 5% for $10,000, you have monthly payments of $53.68, which is exactly the same as a 15y loan at 5% for $6,788.39 (your principal outstanding after 15 years of payments), which would also have monthly payments of $53.68. A few years ago I had a 5 year car   loan. I wanted to prepay it after 2 years and I asked this question to   the lender. I expected a reduction in the interest attached to the car   loan since it didn't go the full 5 years. They basically told me I was   crazy and the balance owed was the full amount of the 5 year car loan.   I didn't prepay it because of this. That is the wrong reason for not prepaying.  I suspect you have misunderstood the terms of the loan - look at the Variable Monthly Payments section above for a discussion.   The best thing to do with all loans is to read the terms carefully and do the calculations yourself in a spreadsheet.  If you are able to get the cashflows spelled out in the contract, then you have understood the loan. First of all any loan will have the last payment be slightly different than the rest. Even if the interest rate is zero it is hard to have a perfect monthly payment amount. By perfect I mean the amount of the loan divided by the number of months would be $ddd.cc0000...  When looking at the amortization table the last payment will either be slightly higher or lower to adjust for the rounding that was done. My suspicion is that the rounding would have resulted in a left over 12 cents. It is also possible that you are paying it off slightly early and the computer is simply taking the leftover amount an spreading it over the remaining period of the loan. You could be paying it early because for the main part of the loan was paid to a company that rounds all payments to the higher dollar, or has a minimum monthly payment amount. I looked at the company you mentioned in the question, and searched the site for an amortization tool. I found it, and used the pre-filled in example. https://www.edfinancial.com/amortizationschedule?pmts=120&intr=6.8&prin=25000 If that last payment is not adjusted the borrower will still owe $0.12. The fact it equals your situation is a coincidence. But is does show what can happen. If you have a 20,000 balance and a 8.75% interest rate, you should be paying between $145 and $150 in interest each month, with the balance going to principal.  (0.0875/12=0.007292, and that times 20,000 is 145.83; as interest is compounded daily, it'll be a little higher than that.)  If the minimum is below $145, then you are not covering the interest; I suspect that is what is happening here, and they're reporting interest paid that wasn't covered in a prior month (assuming you have some months where you only pay the statement minimum, which is less than the total accrued interest). Assuming you're in the US (or most other western countries), your loan servicer should be explaining the exact amount each payment that goes to principal and interest.  I recommend calling them up and finding out exactly why it's not consistent; what should be happening, assuming you pay more than the amount of interest each month, is the interest should go down (very) slowly each month and the amount paying off principal should go up (also slowly).  EG: Etc., until eventually the interest is zero and your loan is paid off.  It probably won't go this quickly for this size of loan - you're only paying off a tiny percentage of principal each month, $50/$20000 or 1/400th - so you won't make too much headway at this rate.   Even adding another $25 would make a huge difference to the length of the loan and the amount of interest paid, but that's another story.   You will eventually at this rate pay off the loan (at $200 a month for all 12 months); this isn't dissimilar to a 30 year mortgage in terms of percent interest to principal (in fact, it's better!).  $50 a month times twelve is $600; 400 payments would take care of it (so a bit over 30 years).  However, as you go you pay more principal and less interest, so you will actually pay it off in 15 years if you continue paying $200 a month exactly. What you may be seeing in your case is a combination of things: In months you pay less (ie, $100, say), the extra $45 in interest needs to go somewhere.  It effectively becomes part of the principal, but from what I've seen that doesn't always happen directly - ie, they account it differently at least for a short time (up to a year, in my experience). This is because of tax laws, if I understand correctly - the amount you pay in interest is tax-deductible, but not the amount of the principal - so it's important for you to have as much called 'interest' as possible.  Thus, if you pay $100 this month and $200 next month, that total of $300 is paying ~$290 of interest and $10 of principal, just as if you'd paid it $150 each month. If you had any penalties, such as for late payments, those come out off the top before interest; they may sometimes take that out as well. All in all, I strongly suggest having an enforced minimum (on your end) of the interest amount at least; that prevents you from being in a situation where your loan grows.  If you can't always hit $200, that's fine; but at least hit $150 every single month.  Otherwise you have a never ending cycle of student loan debt that you really don't want to be in. Separately, on the $1000 payment: As long as you make sure it's not assigned in such a way that the lender only accepts a month's worth at a time (which shouldn't happen, but there are shady lenders), it shouldn't matter what is called 'principal' and what is called 'interest'.  The interest won't go up just because you're making a separate payment (it'll go down!).  The portion that goes to interest will go to paying off the amount of interest you owe from the time of your last payment, plus any accrued but unpaid interest, plus principal.  You won't have the option of not paying that interest, and it doesn't really matter anyway - it's all something you owe and all accruing interest, it only really matters for accounting and taxes.  Double check with your lender (on the phone AND on their website, if possible) that overpayments are not penalized and are applied to principal immediately (or within a few days anyway) and you should be fine. Ditto to Victor. The simple rule is: Pay the minimums on all so you don't get any late fees, etc, then pay off the highest interest rate loan first. A couple of special cases do come to mind: If one or more of these are credit cards, then, here in the U.S. at least, credit cards charge you interest on the average daily balance, unless you pay off the balance entirely, in which case you pay zero interest. So for example say you had two credit cards, both with 1% per month interest, with debt of $2000 and $1000. You have $1500 available. Ignoring minimum payments for the moment, if you put that $1500 against the larger balance, you would still pay interest on the full amount for the current month, or $30. But if you paid off the smaller and put the difference against the larger, then your interest for the current month would be only $15. (Either way, your interest for NEXT month would be the same -- 1% of the $1500 remaining balance or $15 -- assuming you couldn't pay off the other card.)  If one or more of the loans are mortgage loans on which you are paying mortgage insurance, then when you get the balance below a certain point -- usually 80% of the original loan amount -- you no longer have to pay mortgage insurance premiums. Thus the amount you are paying on such premiums needs to be factored into the calculation. There may be other special cases. Those are the ones that I've run into. Yes, by paying double the amount each month you would have in effect paid the loan off in less than half the time. For $13000 at 3% over 60 months your monthly repayments would be $233.59. If you double your monthly repayments to $467.18 you would end up paying the loan off by the end of the 29th months, more than halving your loan term, as long as there are no penalties for paying the loan off early.