help with how a loan repayment is calculated
"It appears the interest is not compounded daily.  Each period of interest has the loan amount calculated on the ""capital"" remaining on the start of period, for each day in the period.  The Excel finance functions don't handle irregular periods that well, but I can reconstruct the interest calculations:" 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.
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. 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 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's no standard formula. You can compare the going rates on the market for unsecured LOCs and take that as the starting anchor. Unsecured lines of credit run in the US at about 8-18%. Your risk should be reflected in the rate, and I see no reason why the rate would change throughout the loan. As to the amount of principal changing? Just chose one of the standard compounding options - daily (most precise, but most tedious to calculate), monthly average balance, etc. What matters is the combination of the loan amount and the time (hours/days/whatever) you've loaned out the money.  $100 * 10 hours * 30 times = 30K dollar-hours  The other loan is $100 * 24 hours * 30 days = 72K dollar-hours  But using your math the original loan is 30X the amount of the second. Assuming that partial payments are held (without interest) until enough money has accumulated to make at least a full payment, and assuming that overpayments are applied toward principal, a strategy of making three $ 96.00 payments per month will shorten your amortization period by less than one month.  These calculations assume that the interest rate is 12.5 percent APR, compounded monthly (with an APY of 13.2416 percent). Instead of 71 payments of $ 285.56 plus a final payment of $ 285.38, you would make the equivalent of 71 payments of $ 288.00 plus a final payment of $ 28.10. If you make one $ 96.00 payment every ten days, you will make an average of 36.5… partial payments per year, instead of 36 partial payments per year.  This will speed up your loan amortization by about another month-and-a-half over the course of the 72 month loan.  One month of shortening is due to the extra principal payments, and the other half-month is due to interest savings.   To a second approximation, this strategy is similar to paying $ 292.00 per month for 69 months plus a final payment of $ 195.38.  In other words, this strategy will probably involve about 212 payments of $ 96.00 each, possibly with a small 213th payment. 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 Question is, what is this number 0.01140924 13.69/12=0.01140924 In addition, how does one come out with the EIR as 13.69% pa? When calculating payments, PV = 9800, N=36 (months), PMT=333.47, results in a rate of 1.140924% per period, and rate of 13.69%/yr. No idea how they claim 7.5% In Excel, type =RATE(36,333.47,-9800,0,0) And you will get 1.141% as the result.  36 = #payments, 333.47 = payment per period, -9800 is the principal (negative, remember this) And the zeros are to say the payments are month end, second zero is the guess.  Edit - I saw the loan is from a Singapore bank. It appears they have different rules on the rates they quote. As quid's answer showed the math, here's the bank's offer page -  The EIR is the rate that we, not just US, but most board members, are used to. I thought I'd offer an example using a 30 year mortgage.   Yo can see above, a 6% fixed rate somehow morphs into a 3.86% AR. No offense to the Singapore bankers, but I see little value in this number. What surprises me most, is that I've not seen this before.  What's baffling is when I change a 15yr term the AP drops to less than half. It's still a 6% loan and there's nothing about it that's 2 percent-ish, in my opinion.  Now we know. What you want to do is figure out how much you're paying in interest, solely (ie, the interest part of each payment), add that up over 48 months, then figure out the net value of the cash inflow/outflow for the points over 48 months (ie, 3.5% annual return on the positive or negative value).  Sum those two.  Then you can see your P&L, and your total cash outflow (up to you if you add a % to your negative initial outflow, and how exactly you consider your $2k closing costs; I agree with JoeTaxpayer about adding at least closing costs to the loan amount.  If you have money to pay the points that would otherwise be earning money, you could alternately consider it a negative cash (ie, instead of accruing 3.5% it's a negative balance accruing that). In excel I'd do something like: Then track changes in H and I when you change columns B and C and G. "I got $3394.83 The first problem with this is that it is backwards.  The NPV (Net Present Value) of three future payments of $997 has to be less than the nominal value.  The nominal value is simple:  $2991.   First step, convert the 8% annual return from the stock market to a monthly return.  Everyone else assumed that the 8% is a monthly return, but that is clearly absurd.  The correct way to do this would be to solve for m in  But we often approximate this by dividing 8% by 12, which would be .67%.  Either way, you divide each payment by the number of months of compounding.   Sum those up using m equal to about .64% (I left the calculated value in memory and used that rather than the rounded value) and you get about $2952.92 which is smaller than $2991.   Obviously $2952.92 is much larger than $2495 and you should not do this.  If the three payments were $842.39 instead, then it would about break even.   Note that this neglects risk.  In a three month period, the stock market is as likely to fall short of an annualized 8% return as to beat it.  This would make more sense if your alternative was to pay off some of your mortgage immediately and take the payments or yp pay a lump sum now and increase future mortgage payments.  Then your return would be safer.   Someone noted in a comment that we would normally base the NPV on the interest rate of the payments.  That's for calculating the NPV to the one making the loan.  Here, we want to calculate the NPV for the borrower.  So the question is what the borrower would do with the money if making payments and not the lump sum.   The question assumes that the borrower would invest in the stock market, which is a risky option and not normally advisable.  I suggest a mortgage based alternative.  If the borrower is going to stuff the money under the mattress until needed, then the answer is simple.  The nominal value of $2991 is also the NPV, as mattresses don't pay interest.  Similarly, many banks don't pay interest on checking these days.  So for someone facing a real decision like this, I'd almost always recommend paying the lump sum and getting it over with.  Even if the payments are ""same as cash"" with no premium charged." Say you buy a bond that currently costs $950, and matures in one year, at $1000 face value. It has one coupon ($50 interest payment) left. The coupon, $50, is 50/950 or 5.26%, but you get the face value, $1000, for an additional $50 return. This is why the yield to maturity is higher than current yield. If the maturity were in two years, the coupons still provide 5.26%, and the extra 1000/950 is another 5.26% over 2 years, or (approx) 2.6%/yr compounded, for a total YTM of 7.86%. This is a back-of envelope calculation, the real way to calculate is with a finance calculator. Entering PV (present value) FV (future value) PMT (coupon payment(s)) and N (number of periods). With no calculator or spreadsheet, my estimate will be pretty close. If it is a business loan, the borrower would be able to claim a deduction for any interest paid on the loan and the lender would include the interest earned as part of their taxable income. You need to be careful on what you do and don't include as income. If the repayments made to you by the borrower in a year is $10,000 but only $8,000 of that is interest and the other $2,000 is part of the principal being returned to the lender, then you would only claim $8,000 as your income and the borrower would only claim $8,000 as a business deduction. Of course if it is interest only, then you and the borrower would use the full $10,000. 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. If you're able to pop this data into excel you can quickly calculate the solution. Every one of these problems boils down to 'Interest Rate', 'Term', 'Payment', 'Present Value', and 'Future Value' (FV will typically be zero). Excel has a formula to calculate any of these components based off of the other inputs.   In this case, the given information is: Interest Rate: 7.56%  Term: 36 Months Monthly PMT: $350 Present Value: ?   You can use the =PV() formula and input the other known values. One caveat is that you'll need to adjust the interest rate to account for the monthly compounding. So, the formula would be =PV(.0063,36,-350). This gives a result of $11,242, which is the amount you'd be able to borrow. [All of these can also be solved on the TI-84+, but I don't have my old calculator on me to walk through the steps]  To calculate the total interest paid, you would then find out how much you'll be paying over the life of the loan. If your monthly payment is $350 for 36 months, the total amount you'd pay is $12,600 ($350*36). Subtract the $11,242 calculated in step one, and you are left with $1,358 worth of interest.   Hope that makes sense. Let me know if you want me to go over any of the steps in more detail. As a former finance student, I would highly recommend locking down the TVM functions, as they will pop up quite often throughout your schooling/career.   Best of luck! 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.