Formula for recalculation of a bad loan, i.e. where payments were missed?
There's not quite enough to answer the question in full. For the two years of non-payment, were there any penalties, or just accrued interest? If no penalties, this is a 3 step time-value-of-money calculation. First, take the terms of the loan and figure out the balance after 5 years.  Second, for two years, increase the balance by the monthly interest rate.  Last, calculate a new payment with a 13 year duration.  Excel or any business calculator can handle this. It sounds like there are no provisions in the loan document for how to proceed in this case.   I would view this as creating a brand new loan. The amount owed is going to be (Principal remaining + interest from 2 years + penalties).  If you created a new loan for 13 years, that would not be how I would expect a lender to behave. I would expect most repayment plans to be something like make double payments until you are caught up or pay an extra $1000 per month until caught up and then resume normal payments.
Easier to copy paste than type this out. Credit: www.financeformulas.net Note that the present value would be the initial loan amount, which is likely the sale price you noted minus a down payment.   The loan payment formula is used to calculate the payments on a loan.   The formula used to calculate loan payments is exactly the same as the   formula used to calculate payments on an ordinary annuity. A loan, by   definition, is an annuity, in that it consists of a series of future   periodic payments. The PV, or present value, portion of the loan payment formula uses the   original loan amount. The original loan amount is essentially the   present value of the future payments on the loan, much like the   present value of an annuity. It is important to keep the rate per period and number of periods   consistent with one another in the formula. If the loan payments are   made monthly, then the rate per period needs to be adjusted to the   monthly rate and the number of periods would be the number of months   on the loan. If payments are quarterly, the terms of the loan payment   formula would be adjusted accordingly. I like to let loan calculators do the heavy lifting for me. This particular calculator lets you choose a weekly pay back scheme. http://www.calculator.net/loan-calculator.html The equation is the same one used for mortgage amortization.  You first want to calculate the PV (present value) for a stream of $50K payments over 20 years at a10% rate.  Then that value is the FV (future value) that you want to save for, and you are looking to solve the payment stream needed to create that future value. Good luck achieving the 10% return, and in knowing your mortality down to the exact year. Unless this is a homework assignment, which need not reflect real life.  Edit - as indicated above, the first step is to get that value in 20 years:  The image is the user-friendly entry screen for the PV calculation. It walks you though the need to enter rate as per period, therefore I enter .1/12 as the rate. The payment you desire is $50K/yr, and since it's a payment, it's a negative number. The equation in excel that results is: =PV(0.1/12,240,-50000/12,0) and the sum calculated is $431,769 Next you wish to know the payments to make to arrive at this number:  In this case, you start at zero PV with a known FV calculated above, and known rate. This solves for the payment needed to get this number, $568.59 The excel equation is: =PMT(0.1/12,240,0,431769) Most people have access to excel or a public domain spreadsheet application (e.g. Openoffice). If you are often needing to perform such calculations, a business finance calculator is recommended. TI used to make a model BA-35 finance calculator, no longer in production, still on eBay, used.  One more update- these equations whether in excel or a calculator are geared toward per period interest, i.e. when you state 10%, they assume a monthly 10/12%. With that said, you required a 20 year deposit period and 20 year withdrawal period. We know you wish to take out $4166.67 per month. The equation to calculate deposit required becomes - 4166.67/(1.00833333)^240= 568.59  HA! Exact same answer, far less work. To be clear, this works only because you required 240 deposits to produce 240 withdrawals in the future. 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 "They're not all ""bad at math borrowers"". How would you like it if you applied for a mortgage, very carefully reviewed all the paperwork, and then the mortgage broker simply transposes your signature to another set of documents with different rates?  People got screwed because the companies often screwed them. For every person with zero income who got a home, who's no worse off now than before, there's dozens who got refinanced and later thrown out on the street when their rates magically reset." 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. Well, what you are asking is EMI, which comes to 30.78 in your case.  The formula you are applying is of compounding a value, which is completely different.  In EMI, person keeps paying money every month or any other period as specified. This amount is firstly allocated towards the interest for the period and the balance for principal amount. So, in effect principal keeps decreasing and subsequently interest thereon. Also, since, interest is getting paid every time it becomes due, compounding actually do not happen at all.  In the case of compounding, interest gets applied at certain interval, but do not get paid. So, in effect every time when interest gets applied, it applies on complete Principal outstanding as well as interest unpaid. Hence, this complete amount gets payable at the end. In this case, total amount payable is obviously high, because of 2 reasons: 1. Since, Principal gets unpaid during whole period, you are paying interest on complete amount for complete period.  2. You will be paying interest on interest (compounding of interest) since you are not paying it as it is becoming due. Hence, both are different. You need to find EMI calculator or EMI formula, to achieve your purpose. EDIT: The formula for calculating EMI: Assuming a loan of Rs. 1 lakh at 9 % per annum, repayable in 15 years, the EMI calculation using the formula will be: EMI = (1,00,000 × 0.0075) × [(1 + 0.0075) 180 ÷ {(1+0.0075) 180 } - 1] = 750 × [3.838 ÷ 2.838] = 750 × 1.35236 = 1,014 "There is no formula that can be applied to most variations of the problem you pose.  The reason is that there is no simple, fixed relationship between the two time periods involved: the time interval for successive payments, and the time period for successive interest compounding. Suppose you have daily compounding and you want to make weekly payments (A case that can be handled).  Say the quoted rate is  4.2% per year, compounded daily Then the rate per day is 4.2/365, or 0.0115068 % So, in one week, a debt would grow through seven compoundings.  A debt of $1 would grow to 1 * (1+.000225068)^7, or 1.000805754 So, the equivalent interest rate for weekly compounding is 0.0805754% Now you have weekly compounding, and weekly payments, so the standard annuity formulas apply. The problem lies in that number ""7"", the number of days in a week.  But if you were trying to handle daily / monthly, or weekly / quarterly, what value would you use? In such cases, the most practical method is to convert any compounding rate to a daily compounding rate, and use a spreadsheet to handle the irregularly spaced payments." The calculation can be made on the basis that the loan is equal to the sum of the repayments discounted to present value.  (For more information see Calculating the Present Value of an Ordinary Annuity.) With Deriving the loan formula from the simple discount summation.  As you can see, this is the same as the loan formula given here. In the UK and Europe APR is usually quoted as the effective interest rate while in the US it is quoted as a nominal rate.  (Also, in the US the effective APR is usually called the annual percentage yield, APY, not APR.) Using the effective interest rate finds the expected answer. The total repayment is £30.78 * n = £1108.08 Using a nominal interest rate does not give the expected answer. 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 Using the facts in your comment: I use the pmt function in excel and the goal seek tool to determine an original balance of ~$24,241.33 Taking into account the statement in the questions that you have paid $6,072.26 in principal gives an estimated current balance of  which almost exactly matches your current balance statement of $18,168.56 a difference of 51 cents. Is it possible that during the time you were in college the accumulated interest caused the balance to grow from 20,800 to 24,241? This could happen if the loans were unsubsidized. 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. 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 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. "Accrued interest generally means ""interest that is earned but not received"" (http://www.businessdictionary.com/definition/accrued-interest.html).  This is the interest that is added on top of the amount that was originally agreed upon. Because your friend missed some months, she will have gained 3% interest on top of the original loan amount for every month that she didn't pay.  The interest even applies to the increased loan amount, so it will increase exponentially for every month that she does not make a payment.  For example, if the loan amount was for $1,000 and she missed the payment the first month, the 3% accrued interest will raise that loan amount to $1030.  If she misses the second month, then the loan amount will become $1060.90 and so on. This means that it will take her more months to pay the loan in its entirety. ""Arrears"" are the overdue payments that she had not made (http://www.investopedia.com/terms/a/arrears.asp). So the sentence ""with susbsequent payments paying the arrears before being applied to the current month's payment"" means that she must pay the overdue debt from the previous months first before she can even make the payment for the current month." The MWRR that you showed in your post is calculated incorrectly. The formula that you use... ($15,750 - $15,000 - $4,000) / ($15,000 + 0.5 x $4,000) Translates into a form of the DIETZ formula of (EMV-BMV-C)/(BMV + .5 x C) The BMV is the STARTING balance. And as a matter of fact, the starting balance was NOT 15,000. It was IN FACT 11,000. See, the starting value for a month MUST BE the ending value of the prior month. So the BMV of 11,000 would give you the correct answer. Because if you added 4,000 at the start of the month (on day 1), it would have to have been ADDED to the 11,000 of the PRIOR month's ENDING value. Make sense? That would also mean that the addition of 4000 to the 11000 would imply that you started day 1 with 11,000. Make sense? Summary: When doing the calculations, you may use the ending value on the last day of the month to get your EMV. BUT YOU MAY NOT take the ending value on day 1 to get the BMV. That simply can not make sense since you already added a bunch of money during the day. Think about it. Davie