How does the EMI break up into principal and interest components after prepayment of a sum considerably larger than the EMI for a home loan? How is it calculated?
Hi,I am trying to explain the principle on which the reducing rate of interest works. On the basis of this, you can relate to the changes that occur in your repayment schedule after you make some part payments.The reducing rate works in a way such that, with time, when the customer keeps repaying his principal amount and the outstanding principal keeps reducing, the interest to be charged to him should be only on the principal outstanding and not on the entire loan amount that he had taken.We will understand this by an example-Loan amount- 1 lacIRR- 30%Installment type- EMI (equated monthly installments)Tenor- 12 monthsStep 1.Let’s denote the principal and interest components by the letter ‘p’ and interest component letters by ‘i’.So, for the twelve months, the EMIs would be-i1+p1i2+p2i3+p3….upto i12+p12.Step 2.Going by the principle of equated installments-(i1+p1)=(i2+p2)=(i3+p3)….and so on.Step 3.What would be the interest charged for the first month?The principal used is the entire Rs.100000For an year the interest is 30%...i.e. 30% of 100000= 30000For one month it is= 30000/12= 2500So, i1=2500Step 4.We know that the interest charged for the second month would be charged only to the remaining principal amount. In equation terms-i2=30% of (100000-p1) divided by 12We also know that all the EMIs are equal.So,i1+p1=i2+p2or2500+p1= i2+p22500+p1= {(100000-p1)*.3/12}+p2Solving the above equation, we will reach upon a relation between p1 and p2.The relation is-p2=(12.3/12)p1 ….applying the same principle to all the principle components we can say that…p3=(12.3/12)p2, p4=(12.3/12)p3……and p12=(12.3/12)p11In simplified terms…every consecutive principal component is equal to 1.025 time of the previous principal component.Step 5.What is the sum of all principal components- definitely equal to the loan amount?Or, we can say that-p1+p2+p3+p4+p5+p6+p7+p8+p9+p10+p11+p12= 100000We can also write this as-p1+(1.025)p1+(1.025)(1.025)p1+(1.025)(1.025)(1.025)p1…..upto the p12= 100000Solving this equation- you will get the value of p1-p1= 7248.713Step 6.Using the value of p1, now we can get the values of all the principal components and also the interest components.This will give you the entire amortization chart for the given parameters.Hope this answers your query.
How to calculate interest and principal?
I assume you are going to make monthly payments to her as opposed to paying it all off at the end of 2 years. The monthly payments are $1,329.62. The first month interest is $150, decreasing by ~$6 per month. The first month principal is $1,179.62, increasing by ~$6 per month. You will pay a total of $1,910.82 interest over the 2 years.
What is principal plus interest? How is it applied and calculated?
Generally when you take a loan from a bank or NBFC (Lending institutions) they will give you a sheet which comprises of the details which you need to pay them back. Mostly it will be on Monthly basis. that is called EMI (Equated Monthly installments).Now if u look into EMI it will be comprising both principle plus EMI. Now let we assume you taken a one lakh loan with the interest 10%. You taken a loan for 5 years i.e., you going to repay the one lakh loan in 1 years with (1 * 12 ) =12 months since you going to repay every monthly for 1 year i am multiplying 1*12So now the loan amount is one lakh then interest rate is 10% let we put calculation in a simpler form but this not following in the banking industry.Now 10% of one lakh rupees is 10,000 rs so you need to repay one lakh ten thousand to bank. now the EMI will be calculated as one 1,00,000/12 =8333.33 then interest amount 10,000 /12 =833.33 (Since one year loan dividing by 12)Now your EMI will be 8333.33+833.33 = 9166.66Here 8333.33 + 833.33 is called principal plus interest. Hope you understand.Note : The above calculation is only for simple understanding method. In real scenario bank will calculate in different method but the concept of Principal plus interest will be same. If they use outstanding balance method then the value of interest and principle will change thats it.
How do I calculate how much goes to principal & interest?
If you have the amortization schedule, you already have the information, but if you really want to know, you first need to know how often the interest is compounded...most compound at least daily, so you would divide the .07 by 365 to get your daily interest. Then multiply your beginning balance for the month by the daily interest times number of days in the month. Other loans just compound on a flat monthly basis, so it is Balance times .07/12 = interest paid. Once you know the interest paid, you subtract it from the payment to get the principle paid. EDIT...using your example, I ran the numbers through an amort calculator...your first payment would consist of $962.50 in interest and $135.25 in principle. Using the above formula, we get $165,000 * .07/12 = $165,000 * .00583 = $962.50. Subtract that from your payment and you get the $135.25. The next month, the balance on the mortgage would be $165,000 - $135.25 = $164,864.75...multiply this by the .00583 and you get $961.71...again what the amort schedule tells us.
What if we calculate the interest on the principal amount continuously in compound interest?
Actually there is an equation derived by Mathematicians to calculate Compound Interest for every instant rather than on Year-on-Year Basis.CI = P * ( e^(r*t) - 1)where CI = Compound Interest P = Principle Amount e = Exponential ~= 2.718 r = Rate of interest (if rate = 4% p.a. then r = 0.04) t = Time in yearsSo clearly, Interest would compound Exponentially instead of a stepwise manner as in YoY basis. Also you would stand to gain more money in the case of continuous compounding of Interest in comparison to YoY basis.The effect of earning 20% annual interest on an initial $1,000 investment at various compounding frequenciesSource of the image : Compound interest
How to find percent paid towards principal and toward interest?
Your question is not very clear but I'll give it a shot here with a couple of possible assumptions as to what you are really looking for. For total per cent of how much of all payments made went to principle simply divide $20,000 by $63727.2. Now if you want what percent of each payment goes to principle you need to get what is called an amortization schedule. You can find these in many places such as Yahoo Finance. Of course in this case the percentage of payment going to principle will change with every payment. The percentage going to principle starts very small but at the end becomes almost 100%. Hope between those two answers you find the answer you are actually looking for.
House Payment: Interest and Principal?
You have to know the (n) number of payments. If the 125,000 is not the buying price or the total price paid at the end of all payment periods then we would have to know at what point in the loan the pay off would be 125,000. To give you some answer I will base this on a 25 year Mortgage. (PV) Previous Value $125,000 (I) Interest 7% (n) Number of Periods 25yrs (pmt) Payment 10,726.31 per yr / 12 Months = $893.86 per month Total amount paid after 25 years = $268,158.00 Price of house $125,000 / 300 months = 416.67 per month Price of house + interest $268,158.00 / 300 months = 893.86 per month Payment on Principal is $416.67 a month Payment on Interest is an additional $477.19 a month Yes as someone said each month the payment that is applied to principal and interest is different. But as an average over the life of the loan the above numbers are correct. In other words the first few payments are all interest but as the loan starts to mature or comes to an end then most all is applied to the principal.
How do I calculate the principal component and interest component of an EMI for a particular month?
There is nothing wrong in the approach you described. There must be a calculation/interpretation mistake in the calculation. It looks like you might have missed out on calculation of interest using outstanding principal instead might have used original principal.Here is another approach that you may try.EMI is calculated like...E = P * r * (((1+r)^n) / (((1+r)^n) -1))Where E = EMIP = principalr = interest rate per monthn = number of monthsOnce you know any 3 of these 4 you can always calculate the 4th.Say you have a 20 yr(240 month) loan and you have already calculated EMI. Now you want to calculate the principal paid in 10th month. Use P = E / (r * (((1+r)^n) / (((1+r)^n) -1)))in place of n put the number of months remaining and you will get the outstanding principal. Use n = 240 - 9 to calculate OS principal before 10th month, and n = 240 - 10 to calculate OS principal after 10th month. The difference between the 2 is the principal amount paid in 10th month.
How do we calculate total simple interest on principal amount?
Advantage 0_O ...i dont see it !!! Your question itself says, ur interest on SI basis is Rs.8 lac & on EMI basis is Rs.4.5lacs approx.So tell me where is the advantage??? There is none !!!Come out of historical / traditional views !!! Now, you might be wondering why is it so ?? Simply because under EMI method , ur principal content is reduced since payment of first installment unlike the simple interest method where ur principal stays the same for the entire duration.
How do banks calculate proportions of principal and interest in each mortgage payment?
for this you can check the mortgage calculators and if you want its formula and calculation then here is this; The following formula is used to calculate the fixed monthly payment (P) required to fully amortize a loan of L dollars over a term of n months at a monthly interest rate of c. [If the quoted rate is 6%, for example, c is .06/12 or .005]. P = L[c(1 + c)n]/[(1 + c)n - 1] The next formula is used to calculate the remaining loan balance (B) of a fixed payment loan after p months. B = L[(1 + c)n - (1 + c)p]/[(1 + c)n - 1] Annual Percentage Rate (APR) Other readers ask about the formula used to calculate the APR. The APR is what economists call an "internal rate of return" (IRR), or the discount rate that equates a future stream of dollars with the present value of that stream. In the case of a home mortgage, the formula is L - F = P1/(1 + i) + P2/(1 + i)2 +… (Pn + Bn)/(1 + i)n Where: i = IRR L = Loan amount F = Points and all other lender fees P = Monthly payment n = Month when the balance is paid in full Bn = Balance in month n This equation can be solved for i only through a series of successive approximations, which must be done by computer. Many calculators will also do it provided that all the values of P are the same.