What does bank do with “Repaid Principal”?
Does it add to their lending reserves or is it utilized in other ways? It depends on how the economy and the bank in particular are doing. To simplify things greatly, banks get deposits and lend (or otherwise invest) the majority of those deposits. They must keep some percentage in reserve in case depositors want to make withdrawals, and if they get a high percentage of withdrawals (pushing them to be undercapitalized) then they may sell their loans to other banks. Whether they lend the money to someone else or use the money for something else will depend completely on how many reserves they have from depositors and whether they have people lined up to take profitable loans from them. I wrote this answer for the benefit of CQM, I'd vote to close this question if I had 49 more reputation points, since it's not really about personal finance.
Lending is not a charitable contribution. Its an investment. If the loan becomes a bad debt - you'll have to show that it had become a bad debt. For example - bankruptcy declaration. You'll have to show an arm's length transaction, for example - real intention to repay (evidenced by payments of principal and interest made). Otherwise if you have an intention for the loan to never be repaid, it is in fact a gift, which is not only not deductible - its taxable. Bottom line - be careful and talk to a EA/CPA to get a proper advice with regards to a specific transaction. Edit to answer your revised question: you're not going to pay taxes if you're not going to have gains. However, if you lose the principal, in addition to the said above you would incur the loss as a personal bad debt, and not business. This is because it is not investment. The difference is in tax treatment: personal bad debt is a short-term capital loss (limited deduction), business is an ordinary loss. Your calculations are correct. It is likely that the bank's software has a rounding error.  In effect, either your bank is overstating your interest by eight cents per month, or your bank is insisting that you prepay your principal by eight cents per month.  If the bank's ongoing interest calculations are correct, your final payment will be slightly smaller (because of the prepaid principal, and because of compound interest on those prepayments).  I have performed similar calculations for my mortgages over the years, and except upon early payoff in the middle of the month, I have always matched my banks' calculations to the penny.  Ironically, this means that my banks' formulas are a bit weird: After making these adjustments, even my calculations for the mid-month payoff matched to the penny. I'd rent and put the $30K/ yr into savings. When the short sale comes off your credit, you'll have a substantial downpayment.  You don't mention the balance, but the current rate you're paying is 3% too high. Even if you get the rate reduced, you have a $100K issue.  I recommend reading through Will Short Sale Prevent Me From Getting VA Home Loan Later? A bit different question, but it talks more about the short sale. A comment for that question makes a key point - if you have a short sale, will the bank chase you for the balance? If not, you have a choice to make.  Adding note after user11043 commented - First, run the numbers. If you were to pay the $100K off over 7 years, it's $1534/mo extra. Nearly $130K, and even then, you might not be at 80% LTV. I don't know what rents are like in your area, but do the math. First, if the rent is less than the current mortgage+property tax and maintenance, you will immediately have better cash flow each month, and over time, save towards the newer house.  If you feel compelled to work this out and stay put, I'd go to the bank and tell them you'd like them to recast the loan to a new rate. They have more to lose than you do, and there's nothing wrong with a bit of a threat. You can walk away, or they can do what's reasonable, to just fix your rate. With a 4% rate, you'd easily attack the principal if you wish. As you commented above, if the bank offers no option, I'd seriously consider the short sale. There's nothing wrong with that option from a moral standpoint, in my opinion. This is not Bedford Falls, and you are not hurting your neighbors. The bank is amoral, if not immoral. What is the formula for calculating the total cost of a loan with extra payments towards the principal? The formula you require is the standard one for calculating the time to repay.  With larger repayments the time to completely repay the loan is reduced. Where The total cost of the loan is then n * d. Explanation & Calculation The formula for a loan is derived from the sum of the cash flows discounted to present value being equal to the principal.  For further info see the section here titled: Calculating the Present Value of an Ordinary Annuity The summation can be reduced to a closed form by induction:  Rearranging for d and n With the OP's figures The original monthly repayment is $1,006.96 Adding $200 each month ... With the higher repayment the loan is repaid in 257.36 months instead of 360.  (Of course a bank would simply take a reduced payment in month 258, but the amounts work out the same.) The saving is $51,882.37 Addendum If the repayments increase was made part-way through the term of the loan the summation and formula would be  Where Then For example, if for the first ten years the payments are $1,006.96 and for the remaining time the repayments are $1,206.96 The loan is completely repaid in 302.528 months. The saving is Plotting over a range of m months: "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." The government gets part of it. The remainder:  Borrower relief will be in the form of mortgage modifications, including first-lien principal and forbearance forgiveness and second-lien extinguishments, low- to moderate-income mortgage originations, and community reinvestment and neighborhood stabilization efforts, with initiatives focused on communities experiencing, or at risk of, urban blight. This includes lien releases, uninhabitable and abandoned property demolition, and remediation and property donations. Also, Bank of America will support the expansion of available affordable rental housing. Bank of America has committed to complete delivery of the relief by no later than August 31, 2018. The consumer relief will be subject to oversight by an independent monitor. - See more at: http://newsroom.bankofamerica.com/press-releases/corporate-and-financial-news/bank-america-reaches-comprehensive-settlement-us-departm#sthash.AR7aJl3o.dpuf your money in a bank gets used to fund other investments. So basically you either make money, or you're making money for someone else.  Sorry i'm such a dick for not foreseeing 100,000% APR interest in bank accounts with no inflation, god i feel stupid now. So this method makes sense and is reasonable and possible.  The money multiplier effect ends up capped by the fact that the bank can only lend a percent of its 'cash'.    My issue understanding this is I've been told that banks actually don't hold 10% of the cash and lend the other 90% but instead hold the full 100% in cash and lend 900%.  Is this accurate?  The issue I see with it is that it becomes exponential growth that is uncapped.  If the bank lends 900%, it has created this money from nothing, which by itself isn't different that the bank loaning 90% and keeping 10%.  The issue comes because the next bank who gets that money deposited will treat that amount as cash as well, so they loan 900% of the 900%.  And so on and so forth.  How does the system prevent this from happening?