How to calculate the number of months until a loan is paid off (given principal, APR and payment amount)?
The formula for determining the number of payments (months) you'll need to make on your loan is:  where i=monthly interest rate (annual rate / 12), A=loan amount (principal), and P=monthly payment. To determine the total interest that you will pay, you can use the following formula:  where P=monthly payment, N=number of payments (from above formula), and A=loan amount (principal). A quick example: using the numbers in the screenshot above ($10,000 loan, $500 monthly payment, 10% APR), the number of payments ends up to be 21.97 (which means that payment number 22 is slightly less than the rest).  In the second formula, you take that number times your $500 payment and determine that you have paid $10,984.81 over the course of the entire loan period.  Subtracting the principal, you have paid $984.81 in total interest. On your spreadsheet, the function you are looking for is NPER: NPER(rate, payment_amount, present_value, [future_value, end_or_beginning]) rate - The interest rate. (This should be the monthly rate, or the annual rate divided by 12.) payment_amount - The amount of each payment made. (For a loan payment, this should be a negative number.) present_value - The current value of the annuity. (The initial principal of the loan) future_value - [ OPTIONAL ] - The future value remaining after the final payment has been made.  (This should be 0, the default if omitted.) end_or_beginning - [ OPTIONAL - 0 by default ] - Whether payments are due at the end (0) or beginning (1) of each period. Here is the derivation of the formula, with The loan is equal to the sum of the repayments discounted to present value.
"a link to this article grabbed my Interest as I was browsing the site for something totally unrelated to finance.  Your question is not silly - I'm not a financial expert, but I've been in your situation several times with Carmax Auto Finance (CAF) in particular. A lot of people probably thought you don't understand how financing works - but your Car Loan set up is EXACTLY how CAF Financing works, which I've used several times. Just some background info to anyone else reading this - unlike most other Simple Interest Car Financing, with CAF, they calculate per-diem based on your principal balance, and recalculate it every time you make a payment, regardless of when your actual due date was.  But here's what makes CAF financing particularly fair - when you do make a payment, your per-diem since your last payment accrued X dollars, and that's your interest portion that is subtracted first from your payment (and obviously per-diem goes down faster the more you pay in a payment), and then EVerything else, including Any extra payments you make - goes to Principal. You do not have to specify that the extra payment(S) are principal only. If your payment amount per month is $500 and you give them 11 payments of $500 - the first $500 will have a small portion go to interest accrued since the last payment - depending on the per-diem that was recalculated, and then EVERYTHING ELSE goes to principal and STILL PUSHES YOUR NEXT DUE DATE (I prefer to break up extra payments as precisely the amount due per month, so that my intention is clear - pay the extra as a payment for the next month, and the one after that, etc, and keep pushing my next due date). That last point of pushing your next due date is the key  - not all car financing companies do that. A lot of them will let you pay to principal yes, but you're still due next month. With CAF, you can have your cake, and eat it too. I worked for them in College - I know their financing system in and out, and I've always financed with them for that very reason.  So, back to the question - should you keep the loan alive, albeit for a small amount. My unprofessional answer is yes! Car loans are very powerful in your credit report because they are installment accounts (same as Mortgages, and other accounts that you pay down to 0 and the loan is closed). Credit cards, are revolving accounts, and don't offer as much bang for your money - unless you are savvy in manipulating your card balances - take it up one month, take it down to 0 the next month, etc. I play those games a lot - but I always find mortgage and auto loans make the best impact.  I do exactly what you do myself - I pay off the car down to about $500 (I actually make several small payments each equal to the agreed upon Monthly payment because their system automatically treats that as a payment for the next month due, and the one after that, etc - on top of paying it all to principal as I mentioned).  DO NOT leave a dollar, as another reader mentioned - they have a ""good will"" threshold, I can't remember how much - probably $50, for which they will consider the account paid off, and close it out. So, if your concern is throwing away free money but you still want the account alive, your ""sweet spot"" where you can be sure the loan is not closed, is probably around $100.  BUT....something else important to consider if you decide to go with that strategy of keeping the account alive (which I recommend). In my case, CAF will adjust down your next payment due, if it's less than the principal left. SO, let's say your regular payment is $400 and you only leave a $100, your next payment due is $100 (and it will go up a few cents each month because of the small per-diem), and that is exactly what CAF will report to the credit bureaus as your monthly obligation - which sucks because now your awesome car payment history looks like you've only been paying $100 every month - so, leave something close to one month's payment (yes, the interest accrued will be higher - but I'm not a penny-pincher when the reward is worth it - if you left $400 for 1.5 years at 10% APR - that equates to about $50 interest for that entire time - well worth it in my books. Sorry for rambling a lot, I suck myself into these debates all the time :)" "The usual rule of thumb is that you should start considering refinance when you can lower the effective interest rate by 1% or more. If you're now paying 4.7% this would mean you should be looking for loans at 3.7% or better to find something that's really worth considering. One exception is if the bank is willing to do an ""in-place refinance"", with no closing costs and no points. Sometimes banks will offer this as a way of retaining customers who would otherwise be tempted to refinance elsewhere. You should still shop around before accepting this kind of offer, to make sure it really is your best option. Most banks offer calculators on their websites that will let you compare your current mortgage to a hypothetical new one. Feed the numbers in, and it can tell you what the difference in payment size will be, how long you need to keep the house before the savings have paid for the closing costs, and what the actual savings will be if you sell the house in any given year (or total savings if you don't sell until after the mortgage is paid off). Remember that In addition to closing costs there are amortization effects. In the early stages of a standard mortgage your money is mostly paying interest; the amount paying down the principal increases over the life of the loan. That's another of the reasons you need to run the calculator; refinancing resets that clock." The first thing you need to do is look at your terms and conditions of your credit card, or ask your bank, how they will apply the payments.  As Dilip notes in his answer, in the US, they will likely apply the minimum payment to the lower rate balance, and then must apply the rest above the minimum to the higher rate balance.  In other countries, this will vary by law and custom.  Do not assume it will pay off the higher balance, or proportionally, without asking. Let's take the following example. You owe $6000.  $5000 is at 13.5% (normal purchase rate) and $1000 is at 22% (cash advance rate).  If your bank applies payments to both balances proportionally, then a payment of $600 will reduce your purchase balance by $500 and your cash advance balance by $100. The average APR, then, is simply sum of the product of the APR times balance.  So here, (.135*5000 + .225*1000)/6000 = 15%.  This is called a weighted average. If the bank applies the payment differently - such as to the lower rate first, or some specified part to the lower rate and the rest to the higher rate - then this will be misleading if you enter it into a calculator, because your average APR will rise over time as you pay off the purchase balance but don't pay off the cash advance balance, or may decrease if the opposite happens. The weighted average is probably reasonably close in the circumstance that you describe, even if you have rules applying the balance differently, so long as they don't 100% pay down the lower rate - so it may be the simplest option for you in terms of rough calculations (where it's not critical to be correct, just close). One approach using the online calculators that might be better, is to treat these like two separate loans/cards.  Many calculators exist for multiple balances.  Then you can allocate funds differently to the two 'cards'.  This would allow you to see how long you will need until you've paid off the higher balance, for example, although it probably won't perfectly match things - unless you find a site that has this specific option available you probably will have to either live with a small error in your calculations or do the math by hand. You've already received good advice here, pay off the highest rate card first, in this case the Best Buy card. I completely agree. To answer your question about the minimum payment, I can't guarantee that this is how Citi does it on your particular card, but several online calculators seem to use the following formula. Minimum Payment = Fees + (APR / 12) x Balance + 1% x Balance. I plugged in your numbers and got really close to the minimum payment you mentioned. I ran calculations for balances of 8,500 and 6,500 and got payments of $184 and $141. You can use this calculator to plug in some numbers for yourself. I found the formula on this page along with a reference stating that Citi uses the formula. Edited to Add: As Bruce Alderman mentioned in his answer, it's probably not a good idea to just pay the minimum. That calculator I linked to shows the difference between paying the minimum and even a small amount ($50 or so) more than the minimum every month. Something like the difference between 3 and 10 years. Two ways to solve this.  Look at the answer. If the answer says 3 months, then using ceiling for similar questions. You have to act according to the exam conventions, not according to own feelings. Whether or not the answer is reasonable and applicable in real life is out of the question.  Ask yourself, did the investment double after 14 years 2 months? i.e. FV >= 2PV. Does a person who ran 99.72 meters in a 100-meter dash counted as touching the finish line? "Taking the last case first, this works out exactly. (Note the Bank of England interest rate has nothing to do with the calculation.) The standard loan formula for an ordinary annuity can be used (as described by BobbyScon), but the periodic interest rate has to be calculated from an effective APR, not a nominal rate.  For details, see APR in the EU and UK, where the definition is only valid for effective APR, as shown below. 2003 BMW 325i £7477 TYPICAL APR 12.9% 60 monthly payments £167.05 How does this work? See the section Calculating the Present Value of an Ordinary Annuity.  The payment formula is derived from the sum of the payments, each discounted to present value. I.e. The example relates to the EU APR definition like so.  Next, the second case doesn't make much sense (unless there is a downpayment). 2004 HONDA CIVIC 1.6 i-VTEC SE 5 door Hatchback £6,999 £113.15 per month ""At APR 9.9% [as quoted in advert], 58 monthly payments"" 58 monthly payments at 9.9% only amount to £5248.75 which is £1750.25 less than the price of the car. Finally, the first case is approximate. 2005 TOYOTA COROLLA 1.4 VVTi 5 door hatchback £7195 From £38 per week ""16.1% APR typical, a 60 month payment, 260 weekly payments"" A weekly payment of £38 would imply an APR of 14.3%." Your goal of wanting to eliminate your debts early is great. Generally, you can save more money by paying off loans with higher interest rates first. However, it sounds like you are excited about the idea of eliminating one of your car loans in two months.  There is nothing wrong with that; it is good to be excited about eliminating debt.  I like your plan. Pay off the $14.6k loan first, then apply the $635 monthly payment to the $19.4k loan.  You'll have that loan paid off almost 3 years early.  Perhaps you'll find some additional money to apply to it and get rid of it even earlier. After you've eliminated both car loans, save up that $1000/month for your next car.  That will allow you to pay cash for it, which will allow you to negotiate the best price and save interest.  0% loans are not free money. Other answers will tell you to wait as long as possible to pay off your 0% loan, but I think there can be good reasons to eliminate smaller loans first, regardless of interest. 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: