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."
If they short the contract, that means, in 5 months, they will owe if the price goes up (receive if the price goes down) the difference between the price they sold the future at, and the 3-month Eurodollar interbank rate, times the value of the contract, times 5. If they're long, they receive if the price goes up (owe if the price goes down), but otherwise unchanged. Cash settlement means they don't actually need to make/receive a three month loan to settle the future, if they held it to expiration - they just pay or receive the difference.  This way, there's no credit risk beyond the clearinghouse. The final settlement price of an expiring three-month Eurodollar futures (GE) contract is equal to 100 minus the three-month Eurodollar interbank time deposit rate. Reading Great Lakes' page How Payments Are Applied, I think you are probably correct about how the payments are applied: Interest first, minimum on each loan next, then any extra is applied to the highest interest loan.  If I were you, I would make one payment a month, and I would make that payment as large as I possibly could. Trying to make more than one payment in a month is too complicated (and you aren't sure exactly how those payments get credited), and saving up for a big payment every few months is pointless and will cost you interest. Since the compounding period and payment period differs (Compounded Daily vs Paid Monthly), you need to find the effective interest rate for one payment period (month).   This means that each month you pay 0.33387092772% of the outstanding principal as interest.  Then use this formula to find the number of months:  Where PV = 21750, Pmt = 220, i = 0.0033387092772  That gives 120 Months.  Depending on the day count convention, (30/360 or 30.416/365 or Actual/Actual), the answer may differ slightly. Using Financial Calculator gives extremely similar answer.  The total cash paid in the entire course of the loan is 120 x $220 = $26,400 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] You need the Present Value, not Future Value formula for this. The loan amount or 1000 is paid/received now (not in the future). The formula is $ PMT = PV (r/n)(1+r/n)^{nt} / [(1+r/n)^{nt} - 1] $  See for example http://www.calculatorsoup.com/calculators/financial/loan-calculator.php With PV = 1000, r=0.07, n=12, t=3 we get PMT = 30.877 per month With the $2000 downpayment and interest rate of 11.5% nominal compounded monthly the monthly payments would be $970.49 As you state, that is a monthly rate of 0.9583% Edit With the new information, taking the standard loan equation where Let Now setting s = 98000, with d = 990.291 solve for r "I feel that getting money sooner than later is always advantageous. If I offered you the choice between getting: Which option would you take? I would take the last option. And for the same reason, from a purely-numbers point of view, I would argue that getting paid biweekly is preferable (assuming the the annual salary is pro-rated fairly, and barring any compulsive spending habits). Your calculations suggest to me that they are trying to answer the question, ""Looking at a single year or month (or some other fixed amount of time) in a vacuum, is there any financial benefit to being paid bi-weekly over monthly?"". The analysis seems to be focusing on comparing the two pay schedules on a month-by-month basis, noting when one is paid bi-weekly, some months you get paid more times than the other. However, one could also compare the two pay schedules on a fortnight-by-fortnight basis, and note that when one is paid monthly, many fortnights you don't get paid at all, and some you get paid a lot. Or one could compare the two pay schedules on an hour-by-hour basis, too. But in the long run, the money adds up to be the same amount. I prefer getting it as soon as I can." "One way to think of the typical fixed rate mortgage, is that you can calculate the balance at the end of the month. Add a month's interest (rate times balance, then divide by 12) then subtract your payment. The principal is now a bit less, and there's a snowball effect that continues to drop the principal more each month.  Even though some might object to my use of the word ""compounding,"" a prepayment has that effect. e.g. you have a 5% mortgage, and pay $100 extra principal. If you did nothing else, 5% compounded over 28 years is about 4X. So, if you did this early on, it would reduce the last payment by about $400. Obviously, there are calculators and spreadsheets that can give the exact numbers.  I don't know the rules for car loans, but one would actually expect them to work similarly, and no, you are not crazy to expect that. Just the opposite." The formula you need is:    M = (r * PV) / (1 - ((1+r)^(-n)))    M = monthly payment ($350)  r = interest per period (7.56% / 12) = 0.63%  n = number of periods (36 months)  PV = present value, or here, your max loan amount given M    Therefore:  $350 = (0.63% * PV) / (1 - ((1+0.63%)^(-36)))   The denominator on the right ends up equal to ~ 0.2025 when you do the math in your calculator. Carry that over to the by multiplying both sides of the equation by 0.2025    This results in $70.82 = 0.63% * PV    Divide $70.82 by 0.63% to get PV = $11,242 (roughly).    Hope this helps explain it algebraically!! One option is to try to get a month ahead on your mortgage payments.  Rather than using the current month's rent to pay the current month's mortgage payments, try to use the previous month's rent to pay the current month's mortgage payments.  This should allow you to pay on time rather than late but not unacceptably late. This is of course using 'new math'.  Namely, if I lend you $100 and you keep it for a month, I've lent you $100.  In fact, if I loan you $100 for a year I've loaned you $100.  But if I lend you $100 overnight, you pay me back in the morning, I lend you $100 overnight, you pay me back in the morning and we repeat that for a month, I've supposedly lent you $3,000.    That's some interesting math for sure. "You'd have to check the terms of your contract. On most installment loans, I think, they calculate interest monthly, not daily. That is, if you make 3 payments of $96 over the course of the month instead of one payment of $288 at the end of the month (but before the due date), it makes absolutely zero difference to their interest calculation. They just total up your payments for the month. That's how my mortgage works and how some past loans I've had worked. All you'd accomplish is to cost yourself some time, postage if you're mailing payments, and waste the bank's time processing multiple payments. If the loan allows you to make pre-payments -- which I think most loans today do -- then what DOES work is to make an extra payment or an overpayment. If you have a few hundred extra dollars, make an extra payment. This reduces your principle and reduces the amount of interest you pay every month for the remainder of the loan. And if you're paying $1 less in interest, then that extra dollar goes against principle, which further reduces the amount you pay in interest the next month. This snowballs and can save you a lot in the long run. Better still, instead of paying $288 each month, pay, say, $300. Then every month you're nibbling away at the principle faster and faster. For example, I calculate that if you're paying $288 per month, you'll pay the loan off in 72 months and pay a total of $6062 in interest. Pay $300 per month and you'll pay it off in 67 months with a total of $6031 interest. Okay, not a huge deal. Pay $350 per month and you pay it off in 55 months with $5449 interest. (I just did quick calculations with a spreadsheet, not accurate to the penny, but close enough for comparison.) PS This is different from ""revolving credit"", like credit cards, where interest is calculated on the ""average daily balance"". With a credit card, making multiple payments would indeed reduce your interest. But not by much. If you pay $100 every 10 days instead of $300 at the end, then you're saving the interest on 20 days x $100 + 10 days x $100, so 12.5% = 0.03% per day, so 0.03% x ($2000+$1000) = 90 cents. If you're mailing your payments, the postage is 49 cents x 2 extra payments = 98 cents. You're losing 8 cents per month by doing this." Not that I doubted everyone's assumption but I wanted to see the math so I did some spreadsheet hacking. I assumed a monthly payments for 30 years which left us with total payments of 483.89.  I then assumed we'd pay an extra $200/month in one of two scenarios.  Scenario 1 we just paid that $200 directly to the lender.  In scenario 2 we set the extra $200 aside every month until we were able to pay off the $10k at 7%.  I assumed that the minimum payments were allocated proportionately and the overpayments were allocated evenly.  That meant we paid off loan 5 at about month 77, loan 4 in month 88, loan 3 in month 120, loan 2 in month 165, and loan 1 in month 170. Getting over to scenario 2 where we pay $483.89 to lender and save $200 separately.  In month 48 we've saved $9600 relative to the principle remaining in loan 3 of $9547.  We pay that off and we're left with loan 1,2,4,5 with a combined principle of about $60930.  At this point we are now going to make payments of 683.89 instead of saving towards principle.  Now our weighted average interest rate is 6.800% instead of 6.824%.  We can calculate the number of payments left given a principle of 60930, interest of 6.8%, and payment of 683.89 to be 124.4 months left for a total of 172.4 months Conclusion: Scenario 1 pays off the debt 3 months sooner with the same monthly expenditure as scenario 2. Unless you are getting the loan from a loan shark, it is the most common case that each payment is applied to the interest accrued to date and the rest is applied towards reducing the principal.  So, assuming that fortnightly means 26 equally-spaced payments during the year, the interest accrued at the end of the first fortnight is $660,000 x (0.0575/26) = $1459.62 and so the principal is reduced by $2299.61 - $1459.62 = $839.99 For the next payment, the principal still owing at the beginning of that fortnight will be $660,000-$839.99 = $659,160.01 and the interest accrued will be $659,160.01 x (0.0575/26) = $1457.76 and so slightly more of the principal will be reduced than the $839.99 of the previous payment.  Lather, rinse, repeat until the loan is paid off which should occur at the end of 17.5 years (or after 455 biweekly payments). If the loan rate changes during this time (since you say that this is a variable-rate loan), the numbers quoted above will change too. And no, it is not the case that just %5.75 of the $2300 is interest, and the rest comes off the principle (sic)? Interest is computed on the principal amount still owed ($660,000 for starters and then decreasing fortnightly). not the loan payment amount. Edit  After playing around with a spreadsheet a bit, I found that if  payments are made every two weeks (14 days apart) rather than 26 equally spaced payments in one year as I used above, interest accrues at the rate of 5.75 x (14/365)% for the 14 days rather than at the rate of (5.75/26)% for the time between payments as I used above each 14 days, $2299.56 is paid as the biweekly mortgage payment instead of the $2299.61 stated by the OP, then 455 payments (slightly less than 17.5 calendar years when leap years are taken into account) will pay off the loan.  In fact, that 455-th payment should be reduced by 65 cents.  In view of rounding of fractional cents and the like, I doubt that it would be possible to have the last equal payment reduce the balance to exactly 0. tl;dr: Be patient, money is probably sitting somewhere, and it will eventually be credited back to your account. I had a similar problem about 10 years ago.  I sent an international wire transfer, from my own bank account in Germany to my bank account in Central America. I had done this before, and there had been no issues, but in this case, even though all the information was correct, the bank rejected the wire because it was above $10K, and in that case, the bank needs written proof from the owner of the receiving account (me) , and so didn't know where the funds were coming from. I had to call the local Sparkasse bank in Germany, as well as an intermediary bank in London to sort it all out, and in total, had to wait about 3-4 weeks to get the money back in my Sparkasse bank account.  At one point I thought I may never see that money back, especially since there was an intermediary bank to deal with, but it all worked out in the end.