Monthly payment on a compounded daily car loan? [duplicate]
I would like to know how they calculated such monthly payment The formula is:  Your values would come out to be: r = (1+3.06/(100*365))^31-1=0.002602 (converting your annual percentage to a monthly rate equivalent of daily compounded interest) PV = 12865.57 n = 48 Inserting your values into the formula: P = [r*(PV)]/[1-(1+r)^(-n)] P = [0.002602*(12865.57)]/[1-(1.002602)^(-48)] P = 285.47
Let's say I have $10,000, and I invest said monies in mutual fund   XXXXX at $100/share, effectively giving me 100 shares. Now, let's   assume at the end of the year I have a 5% return. My $10,000 is now   $10,500. At what point does my investment benefit from compounded interest?   Monthly? Quarter? Yearly? Does it even benefit? Daily would be my answer as your investment, unless you are selling shares or not re-investing distributions is getting the following day's change that impacts the overall return. Consider how if your fund went up 2% one day and then 2% another day from that $10,000 initial investment. The first gain brings it up to $10,200 and then the second makes it $10,402 where the extra $2 is from the compounding. The key though is that these are generally small movements that have to be multiplied together. Note also that if your fund goes up and down, you may end up down overall given how the returns compound. Consider that your $10,000 goes up 10% to $11,000 and then down 10% to result in $9,900 as the return for up x% and down x% is (1+x)(1-x)=1-x^2 which in this case is 1% as 10% of 10% is 1%. The key is how long do you keep all the money in there so that the next day is applied to that amount rather than resetting back to the initial investment. You've got a great emergency fund built up and no credit card debt. That's something to be proud of. If you didn't already have those two things taken care of, that would be your first priority.  If I were in your situation, I would pay off the student loan. Yes, it's a low interest rate, but you've got the opportunity to pay it off completely and eliminate a monthly payment from your life. Take it.  I don't know if you've already contributed to your Roth IRA for this year or not, but I would set aside $11,000 to cover the max contribution to your Roth IRA for this year and next year.  That leaves about $10,000 left. Do you have any money set aside for your next car? If not, allocate most of this money toward your next car. When you need to buy another car, you will be able to pay cash and avoid a car loan. "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." "Outstanding principal balance is the amount you owe at any given time, not including the amount of interest you need to pay as soon as possible. The ""capitalized interest"" shown is consistent with an average of 13.5 months between when each dollar is borrowed and when the repayment period begins. Suppose you borrow the first half of the money on September 1, 2017 and the second half of the money on February 1, 2017 (5 months later).  At that point, half the money has been accruing interest for 5 months.  On January 1, 2018, half the money accrued interest for 16 months, and half the money accrued interest for 11 months.  The lender now expects you to start repaying the loan, with the first payment due at the end of January 2018 or the beginning of February 2018.  If you make the minimum payments on time, the lender expects you to make 120 monthly payments.  The last monthly payment would be at the end of December 2027 or the beginning of January 2028. The lender (or the website) should provide details about the actual payment plan, grace periods, provisions for handling inability to pay due to unemployment, and other terms. In the United States, most installment loans pretend that (for purposes of calculating interest) every month has 30 days -- even February and July!  Each month, 1/12 of the ""annual percentage rate"" (APR) is charged as interest.  If you do the compounding, a 6.8 percent APR corresponds to (1 + 0.068 / 12)^12 - 1 = 7.016 percent ""annual percentage yield"" (APY). Also, the APR is understated.  The 6.8 percent applies to the full balance (including the loan fees), even though the borrower only gets the amount minus the loan fees.  The 6.8 percent rate is useful for doing calculations after the loan fees have been charged, though.  These calculations include the capitalized interest and the monthly payment amounts. A true calculation of the APR would take the loan fees into account, and give a higher number than 6.8 percent.  But the corrected APR would not be useful for calculating the capitalized interest, nor for calculating the monthly payment amounts." "Tricky question.  Many car leasing companies like to quote payments by the week or twice a month to make the car sound cheaper to carry.  If the lease or loan is calculated such that interest accrues monthly ""not in advance"" then any payments made prior to the date on which the interest is calculated will reduce the balance and therefore the interest. However, many loans and leases are calculated at the beginning for the whole life of the agreement.  In that case, splitting each payment in half doesn't do anything to reduce the interest built in to the payments because the interest is calculated ""in advance""" 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. Buy a modest vehicle with a manageable payment.  Keep the payment low enough ($200-300/month) to keep your DTI (Debt-To-Income) ratio clear.  The short-term ding to your credit for new credit should disappear in 3-6 months (your time horizon).  Having a mix of credit is part of the credit scoring model, so having an installment loan is not a bad thing.  Relax. "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."