Calculate a weekly payment on a loan when payment is a month away
Using the standard loan formula with 21% APR nominal, compounded weekly. Calculate an adjusted loan start value by adding 31 - 7 = 24 extra days of daily interest (by converting the nominal compounded weekly rate to a daily rate). For details see Converting between compounding frequencies Applying the standard formula r (pv)/(1 - (1 + r)^-n) = 189.80 So every weekly payment will be 189.80 Alternatively Directly arriving at the same result by using the loan formula described here,  The extension x is 31 - 7 = 24 daily fractions of an average week (where 7 daily fractions of an average week equal one average week). As before, the weekly payment will be 189.80 Both methods are effectively the same calculation. At time = 0, no interest has accrued. That's normal. And the first payment is due after a month, when there's a month's interest and a bit of principal due.  Note - I missed weekly payments. You'd have to account for this manually, add a month's interest, then calculate based on weekly payments. "You'd have to look at the terms of the loan to be sure, but if the interest compounds weekly then you'd have to calculate the effect of 3 compounding periods, then compute for weekly payments. The balance after 3 weeks would be: Using Excel's PMT function for that principal balance, I get a weekly payment of $189.48.   If the interest doesn't compound, the principal balance will be about $8888.37 and the weekly payment would be $189.85. Note, however, that the terms of the loan could be completely customized, so you'd need to be sure that the payment and the amortization schedule make sense to you before you agree to the loan.  Since the interest is very high, I suspect this is a ""no credit needed"" car loan which are notorious for unfavorable (to the borrower) terms."
"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." First, assuming you are making payments for a savings deposit.  The present value of the deposit is the sum of the all the payments discounted to present value.  In this case they would be discounted by the rate of inflation: £100 deposited next year is worth less than £100 today because it will be eroded by inflation.  With a higher rate of inflation the payments are discounted more heavily, so the present value decreases.  A deposit, or annuity due (see Calculating the Present Value of an Annuity Due), can be expressed mathematically like so:-  ∴ by induction  So for example, the following annuity has a present value of £1,136.76 The total amount that will be paid for the annuity is 12 x £100 = £1,200.  With a higher rate of inflation, say 2% per month, and with the same 12 x £100 payments, the present value of the annuity decreases. In Excel (£1,078.68) A similar case is that for a loan, or ordinary annuity (see Calculating the Present Value of an Ordinary Annuity), except the discounting factor is the loan interest rate rather than inflation and repayments are made at the end of each period rather than at the start. The present value of a loan is the value of the all the future repayments discounted to present value.  With a higher interest rate the payments are discounted more heavily, so the present value decreases.  A loan can be expressed mathematically like so:-  ∴ by induction  So for example, the following values fulfill a loan worth £1,125.51 The total amount that will be paid for the loan is 12 x £100 = £1,200.  With a higher rate of interest, say 2% per month, and the same 12 x £100 repayments, the present value of the loan that can be obtained decreases. In Excel (£1,057.53) "I got $3394.83 The first problem with this is that it is backwards.  The NPV (Net Present Value) of three future payments of $997 has to be less than the nominal value.  The nominal value is simple:  $2991.   First step, convert the 8% annual return from the stock market to a monthly return.  Everyone else assumed that the 8% is a monthly return, but that is clearly absurd.  The correct way to do this would be to solve for m in  But we often approximate this by dividing 8% by 12, which would be .67%.  Either way, you divide each payment by the number of months of compounding.   Sum those up using m equal to about .64% (I left the calculated value in memory and used that rather than the rounded value) and you get about $2952.92 which is smaller than $2991.   Obviously $2952.92 is much larger than $2495 and you should not do this.  If the three payments were $842.39 instead, then it would about break even.   Note that this neglects risk.  In a three month period, the stock market is as likely to fall short of an annualized 8% return as to beat it.  This would make more sense if your alternative was to pay off some of your mortgage immediately and take the payments or yp pay a lump sum now and increase future mortgage payments.  Then your return would be safer.   Someone noted in a comment that we would normally base the NPV on the interest rate of the payments.  That's for calculating the NPV to the one making the loan.  Here, we want to calculate the NPV for the borrower.  So the question is what the borrower would do with the money if making payments and not the lump sum.   The question assumes that the borrower would invest in the stock market, which is a risky option and not normally advisable.  I suggest a mortgage based alternative.  If the borrower is going to stuff the money under the mattress until needed, then the answer is simple.  The nominal value of $2991 is also the NPV, as mattresses don't pay interest.  Similarly, many banks don't pay interest on checking these days.  So for someone facing a real decision like this, I'd almost always recommend paying the lump sum and getting it over with.  Even if the payments are ""same as cash"" with no premium charged." 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. 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. That's tricky. Typically you lock in the minimum monthly payment when you close the loan. You can pay more but not less. Options: Basically you need to use a time-value-of-money equation to discount the cashflows back to today. The Wikipedia formula will likely work fine for you, then you just need to pick an effective interest rate to use in the calculation. Run each of your amounts and dates though the formula (there are various on-line calculators to pick from, and sum up the values. You did not mention your location or jurisdiction, but a useful proxy for the interest rate would be the average between the same duration mortgage rate and fixed-deposit rate at your bank; it should be close enough for your purposes - although if an actual lawsuit is involved and the sums high enough to have lawyers, it might be worth engaging an accountant as well to defend the veracity of both the calculation and the interest rates chosen. 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.