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.
In this case, it looks like the interest is simply the nominal daily interest rate times number of days in the period. From that you can use a spreadsheet to calculate the total payment by trial and error. With the different number of days in each period, any formula would be very complicated. In the more usual case where the interest charge for each period is the same, the formula is: m=P*r^n*(r-1)/(r^n-1) where * is multiplication ^ is exponentiation / is division (Sorry, don't know if there's a way to show formulas cleanly on here) P=original principle r=growth factor per payment period, i.e. interest rate + 100% divided by 100, e.g. 1% -> 1.01 n=number of payments Note the growth factor above is per period, so if you have monthly payments, it's the rate per month. The last payment may be different because of rounding errors, unequal number of days per period, or other technicalities. Using that formula here won't give the right answer because of the unequal periods, but it should be close. Let's see: r=0.7% times an average of 28.8 days per period gives 20.16% + 1 = 1.2016. n=5 P=500 m=500*1.2016^5*(1.2016-1)/(1.2016^5-1) =167.78 Further off than I expected, but ballpark. I don't see how anyone could give you a hard-and-fast formula, unless they know where to get some applicable statistics. Because several factors here are not a straight calculation. If you don't replace the tires but keeping driving the car, what is the increased probability that you will get into an accident because of the bald tires? How much will bald tires vs new tires affect the selling price of the car? Presumably the longer you drive the car after getting new tires, the less increase this will give to the market value of the car. What's the formula for that? If you keep the car, what's the probability that it will have other maintenance problems? Etc. That said, it's almost always cheaper to keep your current car than to buy a new one. Even if you have maintenance problems, it would have to be a huge problem to cost more than buying a new car. Suppose you buy a $25,000 car with ... what's a typical new car loan these days? maybe 5 years at 5%? So your payments would be about $470 per month. If you compare spending $1000 for new tires versus paying $470 per month on a new car loan, the tires are cheaper within 3 months. The principle is the same if you buy with cash. To justify buying a new car you have to factor in the value of the pleasure you get from a new car, the peace of mind from having something more reliable, etc, mostly intangibles. It looks like the rate on that first loan is 6-2/3%?  When I look at $72000 principal and a $500 payment, I'm seeing a long term, 24 years. Not 60, but not good either.  Yes, as you pay a bit of principal, the next payment has less interest and even more principal.  I hope your degree is in a field that's lucrative. Or that you're able to get a job that qualifies you for loan forgiveness over time. I'm sorry that advice might seem weak, but aside from that, the best I can offer is to live well beneath your means, i.e. continue to live like a student, and make additional payments.  As far as bi-weekly goes, the lender may not accept partial payments. Set aside the money every two weeks and when you have extra money just make an extra payment amount toward principal.  To pay this off as fast as possible, I'd make as high an extra payment as I could each month to the loan with the higher rate. If the rates are the same, pay it off to the one with the lower balance.  With respect to the debt snowballers, followers of The David, say the rates are simply close, say .25% apart, with the lower balance having the lower rate. If you were to pay this one first, it would occur sooner, of course, and free up that monthly payment, helping your cash flow. But, it comes at a cost.  Note - if, as Noah suggests, the rates are the same, I'd advise to make all extra payments toward the lower balance. That will get you to the point where you've freed up that cash flow for other purposes, whether it's to focus on the higher loan, or anything else you need this for. "While I would be very leery of making any Investments in Greece, and if I lived there might want to strongly consider a larger than average investment in 'international' funds (such as an index fund on the US, UK, or German exchanges) Having debt in Greece might not be such a bad thing... if only it was denominated in local currency. The big issue is that right now, you'd be taking out a loan on property in greece, that would be denominated in Euros.  If worse comes to worse, and Greece is kicked out of the EU and forced to go back to the drachma, then you might be in a situation where the bank says ""this loan is in Euros, we want payment in the same"" and if the drachma is plummeting vs the Euro, you could find your earning power (presuming you were then paid in drachma) greatly diminished.. And since you'd be selling the house for drachma, you might be way under-water in terms of the value of the house (due to currency exchange) vs what you owed. Now, if Greece were currently on the drachma, and you were talking about a mortgage in the same, I'd say go for it.  Since what tends to happen when a government has way overspent is they just print more money rather than default.. that tends to lead to inflation, and a falling currency value vs other countries.  None of which is bad for someone with a debt which would be rapidly shrinking due to the effect of inflation. but right now, safer to rent." Perhaps there is no single formula that accounts for all the time intervals, but there is a method to get formulas for each compound interest period. You deposit money monthly but there is interest applied weekly. Let's assume the month has 4 weeks.  So you added x in the end of the first month, when the new month starts, you have x money in your account. After one week, you have x + bx money. After the second week, you have x + b(x + bx) and so on. Always taking the previous ammount of money and multiplying it by the interest (b) you have. This gives you for the end of the second month:  This looks complicated, but it's easy for computers. Call it f(0), that is: It is a function that gives you the ammount of money you would obtain by the end of the second month. Do you see that the future money inputs are given with relation to the previous ones? Then we can do the following, for n>1 (notice the x is the end of the formula, it's the deposit of money in the end of the month, I'm assuming it'll pass through the compound interest only in the first week of the next month):  And then write:  There is something in mathematics called recurrence relation in which we can use these two formulas to produce a simplified one for arbitrary b and n. Doing it by hand would be a bit complicated, but fortunately CASes are able to do it easily. I used Wolfram Mathematica commands: And it gave me the following formula:  All the work you actually have to do is to figure out what will be f(0) and then write the f(n) for n>0 in terms of f(n-1). Notice that I used the command FullSimplify in my code, Mathematica comes with algorithms for simplyfing formulas so if it didn't find something simpler, you probably won't find it by yourself! If the code looks ugly, it's because of Mathematica clipboard formatting, in the software, it looks like this:  Notice that I wrote the entire formula for f(0), but as it's also a recurrence relation, it can be written as:  That is: f(0)=g(4). This should give you much simpler formulas to apply in this method. "The formula you are looking for is pretty complicated. It's given here: http://itl.nist.gov/div898/handbook/eda/section3/eda3661.htm You might prefer to let somebody else do the grunt work for you. This page will calculate the probability for you: http://stattrek.com/online-calculator/normal.aspx. In your case, you'd enter mean=.114, standard deviation=.132, and ""standard score""= ... oh, you didn't say what you're paying on your debt. Let's say it's 6%, i.e. .06. Note that this page will give you the probability that the actual number will be less than or equal to the ""standard score"". Enter all that and click the magic button and the probability that the investment will produce less than 6% is ... .34124, or 34%. The handy rule of thumb is that the probability is about 68% that the actual number will be within 1 standard deviation of the mean, 95% that it will be within 2 standard deviations, and 99.7% that it will be within 3. Which isn't exactly what you want because you don't want ""within"" but ""less than"". But you could get that by just adding half the difference from 100% for each of the above, i.e. instead of 68-95-99.7 it would be 84-98-99.9. Oh, I missed that in a follow-up comment you say you are paying 4% on a mortgage which you are adjusting to 3% because of tax implications. Probability based on mean and SD you gave of getting less than 3% is 26%. I didn't read the article you cite. I assume the standard deviation given is for the rate of return for one year. If you stretch that over many years, the SD goes down, as many factors tend to even out. So while the probability that money in a given, say, mutual fund will grow by less than 3% in one year is fairly high -- the 25 - 35% we're talking here sounds plausible to me -- the probability that it will grow by an average of less than 3% over a period of 10 or 15 or 20 years is much less. Further Thought There is, of course, no provably-true formula for what makes a reasonable risk. Suppose I offered you an investment that had a 99% chance of showing a $5,000 profit and a 1% chance of a $495,000 loss. Would you take it? I wouldn't. Even though the chance of a loss is small, if it happened, I'd lose everything I have. Is it worth that risk for the modest potential profit? I'd say no. Of course to someone who has a billion dollars, this might be a very reasonable risk. If it fails, oh well, that could really cut in to what he can spend on lunch tomorrow." Reinvestment creates a nightmare when it comes time to do taxes, sadly. Tons of annoying little transactions that happened automatically... Here's one article trying to answer your question: http://www.smartmoney.com/personal-finance/taxes/figuring-out-your-cost-basis-when-youve-lost-the-statements-9529/ You could also try this thing: http://www.gainskeeper.com/us/BasisProIndividual.aspx But I couldn't tell you if it would help. If it makes you feel better, brokerages are now required by the IRS to track your basis for you, so for new transactions and assets you shouldn't end up in this situation. Doesn't help with the old stuff ;-) There are programs out there which will let you refinance even when underwater, under the Government's HARP program. You are overpaying by nearly $7,000 per year compared to a refinance to 4.5%. A classic example of how the bubble hurt people who overextended themselves a bit as housing shot up.  The bank risks a $50K loss if you default or short sell this property. I'd go in and sit down with a branch manager and ask what they can do to recast the loan to a lower rate as you are ready, wiling and able to keep the house and make your payments. Good luck.