Even though your monthly EMI payment won't change, the proportion of principal and interest components will change with time. With each successive payment, you'll pay more towards the principal and less in interest. The exact percentage allocated towards payment of the principal depends on the interest rate. The interest component of the EMI would be larger during the initial months and gradually reduce with each payment. The sum of principal amount and interest is divided by the tenure, i.e., number of months, in which the loan has to be repaid. It consists of the interest on loan as well as part of the principal amount to be repaid. The full Python listing to generate the above results is located here.Equated Monthly Installment - EMI for short - is the amount payable every month to the bank or any other financial institution until the loan amount is fully paid off. This programming effort honors the mathematical principle that applications of an established, reliable result should be derived carefully, with as little room for error as possible. The second value, which in principle should be zero, shows the effect of limited precision in computer numerical mathematics. I then apply that payment amount to a round-robin in which a future value is computed, then that future value is applied to tbe problem of computing a present value for the same parameters. In the above test, I compute a payment amount for an ending balance of 100,000 after 200 payment periods. I also created numerical functions for each of the equation forms and tested them for consistency:įpv = lambdify((fv,np,pmt,ir),results)įfv = lambdify((pv,np,pmt,ir),results)įnp = lambdify((pv,fv,pmt,ir),results)įpmt = lambdify((pv,fv,np,ir),results) This arrangement has a number of advantages, among which are a great reduction in effort, and a way to avoid the kinds of transcription errors that make online code listings so unreliable. The idea of the LaTeX generator is that it exploits the existence of MathJax rendering support in this page to display the equations with little struggle or chance for errors. Pprint(str(v) + ' = ' + padspace(latex(q))) # create insertable LaTeX block for Web page Here are the equations for all the directly computable forms this problem can take, including the variations created by choosing payment-at-beginning and payment-at-end. Result: in 10 years (120 months) you will have a balance of \$23,003.87 ( click here to test this result with the calculator above). For the interest rate per period (per month in this case), divide the annual interest rate of 12% by 12 = 1% per month ( is this correct?). The account has a starting balance of \$0.00 and you are planning to deposit \$100 per month. Let's say you want to know how much money you will have in an investment that has an annual interest rate of 12%. These equations are similar to those used to calculate Population Increase, but they allow you to specify interest and payments as separate variables. $ir$ (interest rate) = The per-period interest rate on the account. $pmt$ (payment) = The amount of each periodic payment, usually a negative amount. $np$ (number of periods) = The number of payment periods, usually expressed in months. $fv$ (future value) = The ending balance after the specified number of payment periods ($np$). This number can be zero, positive (when you take out a loan), or negative (when you make a deposit). $pv$ (present value) = The starting balance in an account. The exception, as Isaac Newton discovered, is that interest computation requires iteration and may result in several solutions. With one exception, each kind of problem can be solved immediately, using a well-defined equation. These equations solve problems that involve compound interest.
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